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Simplifying (4x2 + -9)(4x2 + -9) = 0 Reorder the terms: (-9 + 4x2)(4x2 + -9) = 0 Reorder the terms: (-9 + 4x2)(-9 + 4x2) = 0 Multiply (-9 + 4x2) * (-9 + 4x2) (-9(-9 + 4x2) + 4x2 * (-9 + 4x2)) = 0 ((-9 * -9 + 4x2 * -9) + 4x2 * (-9 + 4x2)) = 0 ((81 + -36x2) + 4x2 * (-9 + 4x2)) = 0 (81 + -36x2 + (-9 * 4x2 + 4x2 * 4x2)) = 0 (81 + -36x2 + (-36x2 + 16x4)) = 0 Combine like terms: -36x2 + -36x2 = -72x2 (81 + -72x2 + 16x4) = 0 Solving 81 + -72x2 + 16x4 = 0 Solving for variable 'x'. Factor a trinomial. (9 + -4x2)(9 + -4x2) = 0 Factor a difference between two squares. ((3 + 2x)(3 + -2x))(9 + -4x2) = 0 Factor a difference between two squares. ((3 + 2x)(3 + -2x))(3 + 2x)(3 + -2x) = 0Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Subproblem 3
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 4
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {-1.5, 1.5, -1.5, 1.5}
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