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Simplifying ((x4) + (8(x2)) + 3) = 0 (x4 + (8(x2)) + 3) = 0 Reorder the terms: (3 + (8x2) + x4) = 0 Remove parenthesis around (3 + (8x2) + x4) 3 + (8x2) + x4 = 0 Solving 3 + (8x2) + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + (8x2) + -3 + x4 = 0 + -3 Reorder the terms: 3 + -3 + (8x2) + x4 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + (8x2) + x4 = 0 + -3 (8x2) + x4 = 0 + -3 Combine like terms: 0 + -3 = -3 (8x2) + x4 = -3 The x term is (8x2). Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. (8x2) + 16 + x4 = -3 + 16 Reorder the terms: 16 + (8x2) + x4 = -3 + 16 Combine like terms: -3 + 16 = 13 16 + (8x2) + x4 = 13 Factor a perfect square on the left side: (x2 + 4)(x2 + 4) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x2 + 4) equal to 3.605551275 and -3.605551275.Subproblem 1
x2 + 4 = 3.605551275 Simplifying x2 + 4 = 3.605551275 Reorder the terms: 4 + x2 = 3.605551275 Solving 4 + x2 = 3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x2 = 3.605551275 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = 3.605551275 + -4 x2 = 3.605551275 + -4 Combine like terms: 3.605551275 + -4 = -0.394448725 x2 = -0.394448725 Simplifying x2 = -0.394448725 Reorder the terms: 0.394448725 + x2 = -0.394448725 + 0.394448725 Combine like terms: -0.394448725 + 0.394448725 = 0.000000000 0.394448725 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 4 = -3.605551275 Simplifying x2 + 4 = -3.605551275 Reorder the terms: 4 + x2 = -3.605551275 Solving 4 + x2 = -3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x2 = -3.605551275 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = -3.605551275 + -4 x2 = -3.605551275 + -4 Combine like terms: -3.605551275 + -4 = -7.605551275 x2 = -7.605551275 Simplifying x2 = -7.605551275 Reorder the terms: 7.605551275 + x2 = -7.605551275 + 7.605551275 Combine like terms: -7.605551275 + 7.605551275 = 0.000000000 7.605551275 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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