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Simplifying (x2 + -9)(64x2 + -25) = 0 Reorder the terms: (-9 + x2)(64x2 + -25) = 0 Reorder the terms: (-9 + x2)(-25 + 64x2) = 0 Multiply (-9 + x2) * (-25 + 64x2) (-9(-25 + 64x2) + x2(-25 + 64x2)) = 0 ((-25 * -9 + 64x2 * -9) + x2(-25 + 64x2)) = 0 ((225 + -576x2) + x2(-25 + 64x2)) = 0 (225 + -576x2 + (-25 * x2 + 64x2 * x2)) = 0 (225 + -576x2 + (-25x2 + 64x4)) = 0 Combine like terms: -576x2 + -25x2 = -601x2 (225 + -601x2 + 64x4) = 0 Solving 225 + -601x2 + 64x4 = 0 Solving for variable 'x'. Factor a trinomial. (25 + -64x2)(9 + -1x2) = 0 Factor a difference between two squares. ((5 + 8x)(5 + -8x))(9 + -1x2) = 0 Factor a difference between two squares. ((3 + x)(3 + -1x))(5 + 8x)(5 + -8x) = 0Subproblem 1
Set the factor '(5 + 8x)' equal to zero and attempt to solve: Simplifying 5 + 8x = 0 Solving 5 + 8x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 8x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8x = 0 + -5 8x = 0 + -5 Combine like terms: 0 + -5 = -5 8x = -5 Divide each side by '8'. x = -0.625 Simplifying x = -0.625Subproblem 2
Set the factor '(5 + -8x)' equal to zero and attempt to solve: Simplifying 5 + -8x = 0 Solving 5 + -8x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -8x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8x = 0 + -5 -8x = 0 + -5 Combine like terms: 0 + -5 = -5 -8x = -5 Divide each side by '-8'. x = 0.625 Simplifying x = 0.625Subproblem 3
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 4
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 = {-0.625, 0.625, -3, 3}
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