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Simplifying (6x2 + -5)(3x2 + -3) = 0 Reorder the terms: (-5 + 6x2)(3x2 + -3) = 0 Reorder the terms: (-5 + 6x2)(-3 + 3x2) = 0 Multiply (-5 + 6x2) * (-3 + 3x2) (-5(-3 + 3x2) + 6x2 * (-3 + 3x2)) = 0 ((-3 * -5 + 3x2 * -5) + 6x2 * (-3 + 3x2)) = 0 ((15 + -15x2) + 6x2 * (-3 + 3x2)) = 0 (15 + -15x2 + (-3 * 6x2 + 3x2 * 6x2)) = 0 (15 + -15x2 + (-18x2 + 18x4)) = 0 Combine like terms: -15x2 + -18x2 = -33x2 (15 + -33x2 + 18x4) = 0 Solving 15 + -33x2 + 18x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(5 + -11x2 + 6x4) = 0 Factor a trinomial. 3((5 + -6x2)(1 + -1x2)) = 0 Factor a difference between two squares. 3((5 + -6x2)((1 + x)(1 + -1x))) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -6x2)' equal to zero and attempt to solve: Simplifying 5 + -6x2 = 0 Solving 5 + -6x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -6x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6x2 = 0 + -5 -6x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -6x2 = -5 Divide each side by '-6'. x2 = 0.8333333333 Simplifying x2 = 0.8333333333 Take the square root of each side: x = {-0.912870929, 0.912870929}Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-0.912870929, 0.912870929, -1, 1}
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