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Simplifying E(x) = (x + 5) * 17(n + 2) * 12(x + -3) * 13(n + -6) * 21 Multiply E * x xE = (x + 5) * 17(n + 2) * 12(x + -3) * 13(n + -6) * 21 Reorder the terms: xE = (5 + x) * 17(n + 2) * 12(x + -3) * 13(n + -6) * 21 Reorder the terms: xE = (5 + x) * 17(2 + n) * 12(x + -3) * 13(n + -6) * 21 Reorder the terms: xE = (5 + x) * 17(2 + n) * 12(-3 + x) * 13(n + -6) * 21 Reorder the terms: xE = (5 + x) * 17(2 + n) * 12(-3 + x) * 13(-6 + n) * 21 Reorder the terms for easier multiplication: xE = 17 * 12 * 13 * 21(5 + x)(2 + n)(-3 + x)(-6 + n) Multiply 17 * 12 xE = 204 * 13 * 21(5 + x)(2 + n)(-3 + x)(-6 + n) Multiply 204 * 13 xE = 2652 * 21(5 + x)(2 + n)(-3 + x)(-6 + n) Multiply 2652 * 21 xE = 55692(5 + x)(2 + n)(-3 + x)(-6 + n) Multiply (5 + x) * (2 + n) xE = 55692(5(2 + n) + x(2 + n))(-3 + x)(-6 + n) xE = 55692((2 * 5 + n * 5) + x(2 + n))(-3 + x)(-6 + n) xE = 55692((10 + 5n) + x(2 + n))(-3 + x)(-6 + n) xE = 55692(10 + 5n + (2 * x + n * x))(-3 + x)(-6 + n) Reorder the terms: xE = 55692(10 + 5n + (nx + 2x))(-3 + x)(-6 + n) xE = 55692(10 + 5n + (nx + 2x))(-3 + x)(-6 + n) xE = 55692(10 + 5n + nx + 2x)(-3 + x)(-6 + n) Multiply (10 + 5n + nx + 2x) * (-3 + x) xE = 55692(10(-3 + x) + 5n * (-3 + x) + nx(-3 + x) + 2x * (-3 + x))(-6 + n) xE = 55692((-3 * 10 + x * 10) + 5n * (-3 + x) + nx(-3 + x) + 2x * (-3 + x))(-6 + n) xE = 55692((-30 + 10x) + 5n * (-3 + x) + nx(-3 + x) + 2x * (-3 + x))(-6 + n) xE = 55692(-30 + 10x + (-3 * 5n + x * 5n) + nx(-3 + x) + 2x * (-3 + x))(-6 + n) xE = 55692(-30 + 10x + (-15n + 5nx) + nx(-3 + x) + 2x * (-3 + x))(-6 + n) xE = 55692(-30 + 10x + -15n + 5nx + (-3 * nx + x * nx) + 2x * (-3 + x))(-6 + n) xE = 55692(-30 + 10x + -15n + 5nx + (-3nx + nx2) + 2x * (-3 + x))(-6 + n) xE = 55692(-30 + 10x + -15n + 5nx + -3nx + nx2 + (-3 * 2x + x * 2x))(-6 + n) xE = 55692(-30 + 10x + -15n + 5nx + -3nx + nx2 + (-6x + 2x2))(-6 + n) Reorder the terms: xE = 55692(-30 + -15n + 5nx + -3nx + nx2 + 10x + -6x + 2x2)(-6 + n) Combine like terms: 5nx + -3nx = 2nx xE = 55692(-30 + -15n + 2nx + nx2 + 10x + -6x + 2x2)(-6 + n) Combine like terms: 10x + -6x = 4x xE = 55692(-30 + -15n + 2nx + nx2 + 4x + 2x2)(-6 + n) Multiply (-30 + -15n + 2nx + nx2 + 4x + 2x2) * (-6 + n) xE = 55692(-30(-6 + n) + -15n * (-6 + n) + 2nx * (-6 + n) + nx2(-6 + n) + 4x * (-6 + n) + 2x2 * (-6 + n)) xE = 55692((-6 * -30 + n * -30) + -15n * (-6 + n) + 2nx * (-6 + n) + nx2(-6 + n) + 4x * (-6 + n) + 2x2 * (-6 + n)) xE = 55692((180 + -30n) + -15n * (-6 + n) + 2nx * (-6 + n) + nx2(-6 + n) + 4x * (-6 + n) + 2x2 * (-6 + n)) xE = 55692(180 + -30n + (-6 * -15n + n * -15n) + 2nx * (-6 + n) + nx2(-6 + n) + 4x * (-6 + n) + 2x2 * (-6 + n)) xE = 55692(180 + -30n + (90n + -15n2) + 2nx * (-6 + n) + nx2(-6 + n) + 4x * (-6 + n) + 2x2 * (-6 + n)) xE = 55692(180 + -30n + 90n + -15n2 + (-6 * 2nx + n * 2nx) + nx2(-6 + n) + 4x * (-6 + n) + 2x2 * (-6 + n)) xE = 55692(180 + -30n + 90n + -15n2 + (-12nx + 2n2x) + nx2(-6 + n) + 4x * (-6 + n) + 2x2 * (-6 + n)) xE = 55692(180 + -30n + 90n + -15n2 + -12nx + 2n2x + (-6 * nx2 + n * nx2) + 4x * (-6 + n) + 2x2 * (-6 + n)) xE = 55692(180 + -30n + 90n + -15n2 + -12nx + 2n2x + (-6nx2 + n2x2) + 4x * (-6 + n) + 2x2 * (-6 + n)) xE = 55692(180 + -30n + 90n + -15n2 + -12nx + 2n2x + -6nx2 + n2x2 + (-6 * 4x + n * 4x) + 2x2 * (-6 + n)) Reorder the terms: xE = 55692(180 + -30n + 90n + -15n2 + -12nx + 2n2x + -6nx2 + n2x2 + (4nx + -24x) + 2x2 * (-6 + n)) xE = 55692(180 + -30n + 90n + -15n2 + -12nx + 2n2x + -6nx2 + n2x2 + (4nx + -24x) + 2x2 * (-6 + n)) xE = 55692(180 + -30n + 90n + -15n2 + -12nx + 2n2x + -6nx2 + n2x2 + 4nx + -24x + (-6 * 2x2 + n * 2x2)) Reorder the terms: xE = 55692(180 + -30n + 90n + -15n2 + -12nx + 2n2x + -6nx2 + n2x2 + 4nx + -24x + (2nx2 + -12x2)) xE = 55692(180 + -30n + 90n + -15n2 + -12nx + 2n2x + -6nx2 + n2x2 + 4nx + -24x + (2nx2 + -12x2)) Reorder the terms: xE = 55692(180 + -30n + 90n + -12nx + 4nx + -6nx2 + 2nx2 + -15n2 + 2n2x + n2x2 + -24x + -12x2) Combine like terms: -30n + 90n = 60n xE = 55692(180 + 60n + -12nx + 4nx + -6nx2 + 2nx2 + -15n2 + 2n2x + n2x2 + -24x + -12x2) Combine like terms: -12nx + 4nx = -8nx xE = 55692(180 + 60n + -8nx + -6nx2 + 2nx2 + -15n2 + 2n2x + n2x2 + -24x + -12x2) Combine like terms: -6nx2 + 2nx2 = -4nx2 xE = 55692(180 + 60n + -8nx + -4nx2 + -15n2 + 2n2x + n2x2 + -24x + -12x2) xE = (180 * 55692 + 60n * 55692 + -8nx * 55692 + -4nx2 * 55692 + -15n2 * 55692 + 2n2x * 55692 + n2x2 * 55692 + -24x * 55692 + -12x2 * 55692) xE = (10024560 + 3341520n + -445536nx + -222768nx2 + -835380n2 + 111384n2x + 55692n2x2 + -1336608x + -668304x2) Solving xE = 10024560 + 3341520n + -445536nx + -222768nx2 + -835380n2 + 111384n2x + 55692n2x2 + -1336608x + -668304x2 Solving for variable 'x'. Reorder the terms: -10024560 + -3341520n + 445536nx + 222768nx2 + 835380n2 + -111384n2x + -55692n2x2 + 1336608x + xE + 668304x2 = 10024560 + 3341520n + -445536nx + -222768nx2 + -835380n2 + 111384n2x + 55692n2x2 + -1336608x + -668304x2 + -10024560 + -3341520n + 445536nx + 222768nx2 + 835380n2 + -111384n2x + -55692n2x2 + 1336608x + 668304x2 Reorder the terms: -10024560 + -3341520n + 445536nx + 222768nx2 + 835380n2 + -111384n2x + -55692n2x2 + 1336608x + xE + 668304x2 = 10024560 + -10024560 + 3341520n + -3341520n + -445536nx + 445536nx + -222768nx2 + 222768nx2 + -835380n2 + 835380n2 + 111384n2x + -111384n2x + 55692n2x2 + -55692n2x2 + -1336608x + 1336608x + -668304x2 + 668304x2 Combine like terms: 10024560 + -10024560 = 0 -10024560 + -3341520n + 445536nx + 222768nx2 + 835380n2 + -111384n2x + -55692n2x2 + 1336608x + xE + 668304x2 = 0 + 3341520n + -3341520n + -445536nx + 445536nx + -222768nx2 + 222768nx2 + -835380n2 + 835380n2 + 111384n2x + -111384n2x + 55692n2x2 + -55692n2x2 + -1336608x + 1336608x + -668304x2 + 668304x2 -10024560 + -3341520n + 445536nx + 222768nx2 + 835380n2 + -111384n2x + -55692n2x2 + 1336608x + xE + 668304x2 = 3341520n + -3341520n + -445536nx + 445536nx + -222768nx2 + 222768nx2 + -835380n2 + 835380n2 + 111384n2x + -111384n2x + 55692n2x2 + -55692n2x2 + -1336608x + 1336608x + -668304x2 + 668304x2 Combine like terms: 3341520n + -3341520n = 0 -10024560 + -3341520n + 445536nx + 222768nx2 + 835380n2 + -111384n2x + -55692n2x2 + 1336608x + xE + 668304x2 = 0 + -445536nx + 445536nx + -222768nx2 + 222768nx2 + -835380n2 + 835380n2 + 111384n2x + -111384n2x + 55692n2x2 + -55692n2x2 + -1336608x + 1336608x + -668304x2 + 668304x2 -10024560 + -3341520n + 445536nx + 222768nx2 + 835380n2 + -111384n2x + -55692n2x2 + 1336608x + xE + 668304x2 = -445536nx + 445536nx + -222768nx2 + 222768nx2 + -835380n2 + 835380n2 + 111384n2x + -111384n2x + 55692n2x2 + -55692n2x2 + -1336608x + 1336608x + -668304x2 + 668304x2 Combine like terms: -445536nx + 445536nx = 0 -10024560 + -3341520n + 445536nx + 222768nx2 + 835380n2 + -111384n2x + -55692n2x2 + 1336608x + xE + 668304x2 = 0 + -222768nx2 + 222768nx2 + -835380n2 + 835380n2 + 111384n2x + -111384n2x + 55692n2x2 + -55692n2x2 + -1336608x + 1336608x + -668304x2 + 668304x2 -10024560 + -3341520n + 445536nx + 222768nx2 + 835380n2 + -111384n2x + -55692n2x2 + 1336608x + xE + 668304x2 = -222768nx2 + 222768nx2 + -835380n2 + 835380n2 + 111384n2x + -111384n2x + 55692n2x2 + -55692n2x2 + -1336608x + 1336608x + -668304x2 + 668304x2 Combine like terms: -222768nx2 + 222768nx2 = 0 -10024560 + -3341520n + 445536nx + 222768nx2 + 835380n2 + -111384n2x + -55692n2x2 + 1336608x + xE + 668304x2 = 0 + -835380n2 + 835380n2 + 111384n2x + -111384n2x + 55692n2x2 + -55692n2x2 + -1336608x + 1336608x + -668304x2 + 668304x2 -10024560 + -3341520n + 445536nx + 222768nx2 + 835380n2 + -111384n2x + -55692n2x2 + 1336608x + xE + 668304x2 = -835380n2 + 835380n2 + 111384n2x + -111384n2x + 55692n2x2 + -55692n2x2 + -1336608x + 1336608x + -668304x2 + 668304x2 Combine like terms: -835380n2 + 835380n2 = 0 -10024560 + -3341520n + 445536nx + 222768nx2 + 835380n2 + -111384n2x + -55692n2x2 + 1336608x + xE + 668304x2 = 0 + 111384n2x + -111384n2x + 55692n2x2 + -55692n2x2 + -1336608x + 1336608x + -668304x2 + 668304x2 -10024560 + -3341520n + 445536nx + 222768nx2 + 835380n2 + -111384n2x + -55692n2x2 + 1336608x + xE + 668304x2 = 111384n2x + -111384n2x + 55692n2x2 + -55692n2x2 + -1336608x + 1336608x + -668304x2 + 668304x2 Combine like terms: 111384n2x + -111384n2x = 0 -10024560 + -3341520n + 445536nx + 222768nx2 + 835380n2 + -111384n2x + -55692n2x2 + 1336608x + xE + 668304x2 = 0 + 55692n2x2 + -55692n2x2 + -1336608x + 1336608x + -668304x2 + 668304x2 -10024560 + -3341520n + 445536nx + 222768nx2 + 835380n2 + -111384n2x + -55692n2x2 + 1336608x + xE + 668304x2 = 55692n2x2 + -55692n2x2 + -1336608x + 1336608x + -668304x2 + 668304x2 Combine like terms: 55692n2x2 + -55692n2x2 = 0 -10024560 + -3341520n + 445536nx + 222768nx2 + 835380n2 + -111384n2x + -55692n2x2 + 1336608x + xE + 668304x2 = 0 + -1336608x + 1336608x + -668304x2 + 668304x2 -10024560 + -3341520n + 445536nx + 222768nx2 + 835380n2 + -111384n2x + -55692n2x2 + 1336608x + xE + 668304x2 = -1336608x + 1336608x + -668304x2 + 668304x2 Combine like terms: -1336608x + 1336608x = 0 -10024560 + -3341520n + 445536nx + 222768nx2 + 835380n2 + -111384n2x + -55692n2x2 + 1336608x + xE + 668304x2 = 0 + -668304x2 + 668304x2 -10024560 + -3341520n + 445536nx + 222768nx2 + 835380n2 + -111384n2x + -55692n2x2 + 1336608x + xE + 668304x2 = -668304x2 + 668304x2 Combine like terms: -668304x2 + 668304x2 = 0 -10024560 + -3341520n + 445536nx + 222768nx2 + 835380n2 + -111384n2x + -55692n2x2 + 1336608x + xE + 668304x2 = 0 The solution to this equation could not be determined.
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