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Simplifying (3 + -6x2)(3 + -6x2) = 0 Multiply (3 + -6x2) * (3 + -6x2) (3(3 + -6x2) + -6x2 * (3 + -6x2)) = 0 ((3 * 3 + -6x2 * 3) + -6x2 * (3 + -6x2)) = 0 ((9 + -18x2) + -6x2 * (3 + -6x2)) = 0 (9 + -18x2 + (3 * -6x2 + -6x2 * -6x2)) = 0 (9 + -18x2 + (-18x2 + 36x4)) = 0 Combine like terms: -18x2 + -18x2 = -36x2 (9 + -36x2 + 36x4) = 0 Solving 9 + -36x2 + 36x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(1 + -4x2 + 4x4) = 0 Factor a trinomial. 9((1 + -2x2)(1 + -2x2)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(1 + -2x2)' equal to zero and attempt to solve: Simplifying 1 + -2x2 = 0 Solving 1 + -2x2 = 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 + -2x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x2 = 0 + -1 -2x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2x2 = -1 Divide each side by '-2'. x2 = 0.5 Simplifying x2 = 0.5 Take the square root of each side: x = {-0.707106781, 0.707106781}Subproblem 2
Set the factor '(1 + -2x2)' equal to zero and attempt to solve: Simplifying 1 + -2x2 = 0 Solving 1 + -2x2 = 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 + -2x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x2 = 0 + -1 -2x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2x2 = -1 Divide each side by '-2'. x2 = 0.5 Simplifying x2 = 0.5 Take the square root of each side: x = {-0.707106781, 0.707106781}Solution
x = {-0.707106781, 0.707106781, -0.707106781, 0.707106781}
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