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Simplifying 116 = -16x2 + 80x + 16 Reorder the terms: 116 = 16 + 80x + -16x2 Solving 116 = 16 + 80x + -16x2 Solving for variable 'x'. Combine like terms: 116 + -16 = 100 100 + -80x + 16x2 = 16 + 80x + -16x2 + -16 + -80x + 16x2 Reorder the terms: 100 + -80x + 16x2 = 16 + -16 + 80x + -80x + -16x2 + 16x2 Combine like terms: 16 + -16 = 0 100 + -80x + 16x2 = 0 + 80x + -80x + -16x2 + 16x2 100 + -80x + 16x2 = 80x + -80x + -16x2 + 16x2 Combine like terms: 80x + -80x = 0 100 + -80x + 16x2 = 0 + -16x2 + 16x2 100 + -80x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 100 + -80x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(25 + -20x + 4x2) = 0 Factor a trinomial. 4((5 + -2x)(5 + -2x)) = 0 Ignore the factor 4.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 '(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 = {2.5, 2.5}
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