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Simplifying 3x2(2x2 + -2) = (-1x2)(5x2 + 2) Reorder the terms: 3x2(-2 + 2x2) = (-1x2)(5x2 + 2) (-2 * 3x2 + 2x2 * 3x2) = (-1x2)(5x2 + 2) (-6x2 + 6x4) = (-1x2)(5x2 + 2) Remove parenthesis around (-1x2) -6x2 + 6x4 = -1x2(5x2 + 2) Reorder the terms: -6x2 + 6x4 = -1x2(2 + 5x2) -6x2 + 6x4 = (2 * -1x2 + 5x2 * -1x2) -6x2 + 6x4 = (-2x2 + -5x4) Solving -6x2 + 6x4 = -2x2 + -5x4 Solving for variable 'x'. Reorder the terms: -6x2 + 2x2 + 6x4 + 5x4 = -2x2 + -5x4 + 2x2 + 5x4 Combine like terms: -6x2 + 2x2 = -4x2 -4x2 + 6x4 + 5x4 = -2x2 + -5x4 + 2x2 + 5x4 Combine like terms: 6x4 + 5x4 = 11x4 -4x2 + 11x4 = -2x2 + -5x4 + 2x2 + 5x4 Reorder the terms: -4x2 + 11x4 = -2x2 + 2x2 + -5x4 + 5x4 Combine like terms: -2x2 + 2x2 = 0 -4x2 + 11x4 = 0 + -5x4 + 5x4 -4x2 + 11x4 = -5x4 + 5x4 Combine like terms: -5x4 + 5x4 = 0 -4x2 + 11x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(-4 + 11x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-4 + 11x2)' equal to zero and attempt to solve: Simplifying -4 + 11x2 = 0 Solving -4 + 11x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + 11x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 11x2 = 0 + 4 11x2 = 0 + 4 Combine like terms: 0 + 4 = 4 11x2 = 4 Divide each side by '11'. x2 = 0.3636363636 Simplifying x2 = 0.3636363636 Take the square root of each side: x = {-0.603022689, 0.603022689}Solution
x = {0, -0.603022689, 0.603022689}
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