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Simplifying 2x(x + -8) = (x + 9)(x + -6) Reorder the terms: 2x(-8 + x) = (x + 9)(x + -6) (-8 * 2x + x * 2x) = (x + 9)(x + -6) (-16x + 2x2) = (x + 9)(x + -6) Reorder the terms: -16x + 2x2 = (9 + x)(x + -6) Reorder the terms: -16x + 2x2 = (9 + x)(-6 + x) Multiply (9 + x) * (-6 + x) -16x + 2x2 = (9(-6 + x) + x(-6 + x)) -16x + 2x2 = ((-6 * 9 + x * 9) + x(-6 + x)) -16x + 2x2 = ((-54 + 9x) + x(-6 + x)) -16x + 2x2 = (-54 + 9x + (-6 * x + x * x)) -16x + 2x2 = (-54 + 9x + (-6x + x2)) Combine like terms: 9x + -6x = 3x -16x + 2x2 = (-54 + 3x + x2) Solving -16x + 2x2 = -54 + 3x + x2 Solving for variable 'x'. Reorder the terms: 54 + -16x + -3x + 2x2 + -1x2 = -54 + 3x + x2 + 54 + -3x + -1x2 Combine like terms: -16x + -3x = -19x 54 + -19x + 2x2 + -1x2 = -54 + 3x + x2 + 54 + -3x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 54 + -19x + 1x2 = -54 + 3x + x2 + 54 + -3x + -1x2 Reorder the terms: 54 + -19x + 1x2 = -54 + 54 + 3x + -3x + x2 + -1x2 Combine like terms: -54 + 54 = 0 54 + -19x + 1x2 = 0 + 3x + -3x + x2 + -1x2 54 + -19x + 1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 54 + -19x + 1x2 = 0 + x2 + -1x2 54 + -19x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 54 + -19x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-54' to each side of the equation. 54 + -19x + -54 + x2 = 0 + -54 Reorder the terms: 54 + -54 + -19x + x2 = 0 + -54 Combine like terms: 54 + -54 = 0 0 + -19x + x2 = 0 + -54 -19x + x2 = 0 + -54 Combine like terms: 0 + -54 = -54 -19x + x2 = -54 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = -54 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -54 + 90.25 Combine like terms: -54 + 90.25 = 36.25 90.25 + -19x + x2 = 36.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (x + -9.5) equal to 6.020797289 and -6.020797289.Subproblem 1
x + -9.5 = 6.020797289 Simplifying x + -9.5 = 6.020797289 Reorder the terms: -9.5 + x = 6.020797289 Solving -9.5 + x = 6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 6.020797289 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 6.020797289 + 9.5 x = 6.020797289 + 9.5 Combine like terms: 6.020797289 + 9.5 = 15.520797289 x = 15.520797289 Simplifying x = 15.520797289Subproblem 2
x + -9.5 = -6.020797289 Simplifying x + -9.5 = -6.020797289 Reorder the terms: -9.5 + x = -6.020797289 Solving -9.5 + x = -6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -6.020797289 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -6.020797289 + 9.5 x = -6.020797289 + 9.5 Combine like terms: -6.020797289 + 9.5 = 3.479202711 x = 3.479202711 Simplifying x = 3.479202711Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.520797289, 3.479202711}
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