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Simplifying 2x2(8x2 + -16) + -4(10x2 + -1) = -77 Reorder the terms: 2x2(-16 + 8x2) + -4(10x2 + -1) = -77 (-16 * 2x2 + 8x2 * 2x2) + -4(10x2 + -1) = -77 (-32x2 + 16x4) + -4(10x2 + -1) = -77 Reorder the terms: -32x2 + 16x4 + -4(-1 + 10x2) = -77 -32x2 + 16x4 + (-1 * -4 + 10x2 * -4) = -77 -32x2 + 16x4 + (4 + -40x2) = -77 Reorder the terms: 4 + -32x2 + -40x2 + 16x4 = -77 Combine like terms: -32x2 + -40x2 = -72x2 4 + -72x2 + 16x4 = -77 Solving 4 + -72x2 + 16x4 = -77 Solving for variable 'x'. Reorder the terms: 4 + 77 + -72x2 + 16x4 = -77 + 77 Combine like terms: 4 + 77 = 81 81 + -72x2 + 16x4 = -77 + 77 Combine like terms: -77 + 77 = 0 81 + -72x2 + 16x4 = 0 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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