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Simplifying 30 = 8x(x + -1) Reorder the terms: 30 = 8x(-1 + x) 30 = (-1 * 8x + x * 8x) 30 = (-8x + 8x2) Solving 30 = -8x + 8x2 Solving for variable 'x'. Reorder the terms: 30 + 8x + -8x2 = -8x + 8x + 8x2 + -8x2 Combine like terms: -8x + 8x = 0 30 + 8x + -8x2 = 0 + 8x2 + -8x2 30 + 8x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 30 + 8x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 4x + -4x2) = 0 Factor a trinomial. 2((5 + -2x)(3 + 2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Solution
x = {2.5, -1.5}
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