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Simplifying 0 = -16x2 + 60x + 16 Reorder the terms: 0 = 16 + 60x + -16x2 Solving 0 = 16 + 60x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -16 = -16 -16 + -60x + 16x2 = 16 + 60x + -16x2 + -16 + -60x + 16x2 Reorder the terms: -16 + -60x + 16x2 = 16 + -16 + 60x + -60x + -16x2 + 16x2 Combine like terms: 16 + -16 = 0 -16 + -60x + 16x2 = 0 + 60x + -60x + -16x2 + 16x2 -16 + -60x + 16x2 = 60x + -60x + -16x2 + 16x2 Combine like terms: 60x + -60x = 0 -16 + -60x + 16x2 = 0 + -16x2 + 16x2 -16 + -60x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -16 + -60x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + -15x + 4x2) = 0 Factor a trinomial. 4((-1 + -4x)(4 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -4x)' equal to zero and attempt to solve: Simplifying -1 + -4x = 0 Solving -1 + -4x = 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 + -4x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4x = 0 + 1 -4x = 0 + 1 Combine like terms: 0 + 1 = 1 -4x = 1 Divide each side by '-4'. x = -0.25 Simplifying x = -0.25Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-0.25, 4}
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