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Simplifying (x2 + -4)(x2 + 4) = (8x2 + -7) Reorder the terms: (-4 + x2)(x2 + 4) = (8x2 + -7) Reorder the terms: (-4 + x2)(4 + x2) = (8x2 + -7) Multiply (-4 + x2) * (4 + x2) (-4(4 + x2) + x2(4 + x2)) = (8x2 + -7) ((4 * -4 + x2 * -4) + x2(4 + x2)) = (8x2 + -7) ((-16 + -4x2) + x2(4 + x2)) = (8x2 + -7) (-16 + -4x2 + (4 * x2 + x2 * x2)) = (8x2 + -7) (-16 + -4x2 + (4x2 + x4)) = (8x2 + -7) Combine like terms: -4x2 + 4x2 = 0 (-16 + 0 + x4) = (8x2 + -7) (-16 + x4) = (8x2 + -7) Reorder the terms: -16 + x4 = (-7 + 8x2) Remove parenthesis around (-7 + 8x2) -16 + x4 = -7 + 8x2 Solving -16 + x4 = -7 + 8x2 Solving for variable 'x'. Reorder the terms: -16 + 7 + -8x2 + x4 = -7 + 8x2 + 7 + -8x2 Combine like terms: -16 + 7 = -9 -9 + -8x2 + x4 = -7 + 8x2 + 7 + -8x2 Reorder the terms: -9 + -8x2 + x4 = -7 + 7 + 8x2 + -8x2 Combine like terms: -7 + 7 = 0 -9 + -8x2 + x4 = 0 + 8x2 + -8x2 -9 + -8x2 + x4 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -9 + -8x2 + x4 = 0 Factor a trinomial. (-1 + -1x2)(9 + -1x2) = 0 Factor a difference between two squares. (-1 + -1x2)((3 + x)(3 + -1x)) = 0Subproblem 1
Set the factor '(-1 + -1x2)' equal to zero and attempt to solve: Simplifying -1 + -1x2 = 0 Solving -1 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x2 = 0 + 1 -1x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1x2 = 1 Divide each side by '-1'. x2 = -1 Simplifying x2 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-3, 3}
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