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Simplifying 60 = -16x2 + 128x Reorder the terms: 60 = 128x + -16x2 Solving 60 = 128x + -16x2 Solving for variable 'x'. Reorder the terms: 60 + -128x + 16x2 = 128x + -128x + -16x2 + 16x2 Combine like terms: 128x + -128x = 0 60 + -128x + 16x2 = 0 + -16x2 + 16x2 60 + -128x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 60 + -128x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(15 + -32x + 4x2) = 0 Factor a trinomial. 4((1 + -2x)(15 + -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 '(15 + -2x)' equal to zero and attempt to solve: Simplifying 15 + -2x = 0 Solving 15 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -2x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -2x = 0 + -15 -2x = 0 + -15 Combine like terms: 0 + -15 = -15 -2x = -15 Divide each side by '-2'. x = 7.5 Simplifying x = 7.5Solution
x = {0.5, 7.5}
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