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Simplifying 8 = -16x2 + 4x + 20 Reorder the terms: 8 = 20 + 4x + -16x2 Solving 8 = 20 + 4x + -16x2 Solving for variable 'x'. Combine like terms: 8 + -20 = -12 -12 + -4x + 16x2 = 20 + 4x + -16x2 + -20 + -4x + 16x2 Reorder the terms: -12 + -4x + 16x2 = 20 + -20 + 4x + -4x + -16x2 + 16x2 Combine like terms: 20 + -20 = 0 -12 + -4x + 16x2 = 0 + 4x + -4x + -16x2 + 16x2 -12 + -4x + 16x2 = 4x + -4x + -16x2 + 16x2 Combine like terms: 4x + -4x = 0 -12 + -4x + 16x2 = 0 + -16x2 + 16x2 -12 + -4x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -12 + -4x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-3 + -1x + 4x2) = 0 Factor a trinomial. 4((-3 + -4x)(1 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve: Simplifying -3 + -4x = 0 Solving -3 + -4x = 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 + -4x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4x = 0 + 3 -4x = 0 + 3 Combine like terms: 0 + 3 = 3 -4x = 3 Divide each side by '-4'. x = -0.75 Simplifying x = -0.75Subproblem 2
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 = {-0.75, 1}
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