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Simplifying 14 = -16x2 + 20x + 50 Reorder the terms: 14 = 50 + 20x + -16x2 Solving 14 = 50 + 20x + -16x2 Solving for variable 'x'. Combine like terms: 14 + -50 = -36 -36 + -20x + 16x2 = 50 + 20x + -16x2 + -50 + -20x + 16x2 Reorder the terms: -36 + -20x + 16x2 = 50 + -50 + 20x + -20x + -16x2 + 16x2 Combine like terms: 50 + -50 = 0 -36 + -20x + 16x2 = 0 + 20x + -20x + -16x2 + 16x2 -36 + -20x + 16x2 = 20x + -20x + -16x2 + 16x2 Combine like terms: 20x + -20x = 0 -36 + -20x + 16x2 = 0 + -16x2 + 16x2 -36 + -20x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -36 + -20x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-9 + -5x + 4x2) = 0 Factor a trinomial. 4((-1 + -1x)(9 + -4x)) = 0 Ignore the factor 4.Subproblem 1
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 = -1Subproblem 2
Set the factor '(9 + -4x)' equal to zero and attempt to solve: Simplifying 9 + -4x = 0 Solving 9 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -4x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4x = 0 + -9 -4x = 0 + -9 Combine like terms: 0 + -9 = -9 -4x = -9 Divide each side by '-4'. x = 2.25 Simplifying x = 2.25Solution
x = {-1, 2.25}
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