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Simplifying (4x2 + -2)(4x2 + -2) = 0 Reorder the terms: (-2 + 4x2)(4x2 + -2) = 0 Reorder the terms: (-2 + 4x2)(-2 + 4x2) = 0 Multiply (-2 + 4x2) * (-2 + 4x2) (-2(-2 + 4x2) + 4x2 * (-2 + 4x2)) = 0 ((-2 * -2 + 4x2 * -2) + 4x2 * (-2 + 4x2)) = 0 ((4 + -8x2) + 4x2 * (-2 + 4x2)) = 0 (4 + -8x2 + (-2 * 4x2 + 4x2 * 4x2)) = 0 (4 + -8x2 + (-8x2 + 16x4)) = 0 Combine like terms: -8x2 + -8x2 = -16x2 (4 + -16x2 + 16x4) = 0 Solving 4 + -16x2 + 16x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + -4x2 + 4x4) = 0 Factor a trinomial. 4((1 + -2x2)(1 + -2x2)) = 0 Ignore the factor 4.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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