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Simplifying -5(x2 + -4)(25 + -1x2) = 0 Reorder the terms: -5(-4 + x2)(25 + -1x2) = 0 Multiply (-4 + x2) * (25 + -1x2) -5(-4(25 + -1x2) + x2(25 + -1x2)) = 0 -5((25 * -4 + -1x2 * -4) + x2(25 + -1x2)) = 0 -5((-100 + 4x2) + x2(25 + -1x2)) = 0 -5(-100 + 4x2 + (25 * x2 + -1x2 * x2)) = 0 -5(-100 + 4x2 + (25x2 + -1x4)) = 0 Combine like terms: 4x2 + 25x2 = 29x2 -5(-100 + 29x2 + -1x4) = 0 (-100 * -5 + 29x2 * -5 + -1x4 * -5) = 0 (500 + -145x2 + 5x4) = 0 Solving 500 + -145x2 + 5x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(100 + -29x2 + x4) = 0 Factor a trinomial. 5((4 + -1x2)(25 + -1x2)) = 0 Factor a difference between two squares. 5(((2 + x)(2 + -1x))(25 + -1x2)) = 0 Factor a difference between two squares. 5(((5 + x)(5 + -1x))(2 + x)(2 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 3
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 4
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-2, 2, -5, 5}
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