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Simplifying (4x2 + -1)(6x2 + -9) = 0 Reorder the terms: (-1 + 4x2)(6x2 + -9) = 0 Reorder the terms: (-1 + 4x2)(-9 + 6x2) = 0 Multiply (-1 + 4x2) * (-9 + 6x2) (-1(-9 + 6x2) + 4x2 * (-9 + 6x2)) = 0 ((-9 * -1 + 6x2 * -1) + 4x2 * (-9 + 6x2)) = 0 ((9 + -6x2) + 4x2 * (-9 + 6x2)) = 0 (9 + -6x2 + (-9 * 4x2 + 6x2 * 4x2)) = 0 (9 + -6x2 + (-36x2 + 24x4)) = 0 Combine like terms: -6x2 + -36x2 = -42x2 (9 + -42x2 + 24x4) = 0 Solving 9 + -42x2 + 24x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -14x2 + 8x4) = 0 Factor a trinomial. 3((1 + -4x2)(3 + -2x2)) = 0 Factor a difference between two squares. 3(((1 + 2x)(1 + -2x))(3 + -2x2)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -2x2)' equal to zero and attempt to solve: Simplifying 3 + -2x2 = 0 Solving 3 + -2x2 = 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 + -2x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x2 = 0 + -3 -2x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -2x2 = -3 Divide each side by '-2'. x2 = 1.5 Simplifying x2 = 1.5 Take the square root of each side: x = {-1.224744871, 1.224744871}Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Subproblem 3
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {-1.224744871, 1.224744871, -0.5, 0.5}
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