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Simplifying 12 = -16x2 + 32x + 32 Reorder the terms: 12 = 32 + 32x + -16x2 Solving 12 = 32 + 32x + -16x2 Solving for variable 'x'. Combine like terms: 12 + -32 = -20 -20 + -32x + 16x2 = 32 + 32x + -16x2 + -32 + -32x + 16x2 Reorder the terms: -20 + -32x + 16x2 = 32 + -32 + 32x + -32x + -16x2 + 16x2 Combine like terms: 32 + -32 = 0 -20 + -32x + 16x2 = 0 + 32x + -32x + -16x2 + 16x2 -20 + -32x + 16x2 = 32x + -32x + -16x2 + 16x2 Combine like terms: 32x + -32x = 0 -20 + -32x + 16x2 = 0 + -16x2 + 16x2 -20 + -32x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -20 + -32x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + -8x + 4x2) = 0 Factor a trinomial. 4((-1 + -2x)(5 + -2x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 2
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 = 2.5Solution
x = {-0.5, 2.5}
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