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Simplifying -16x2 + 24x + 60 = 68 Reorder the terms: 60 + 24x + -16x2 = 68 Solving 60 + 24x + -16x2 = 68 Solving for variable 'x'. Reorder the terms: 60 + -68 + 24x + -16x2 = 68 + -68 Combine like terms: 60 + -68 = -8 -8 + 24x + -16x2 = 68 + -68 Combine like terms: 68 + -68 = 0 -8 + 24x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-1 + 3x + -2x2) = 0 Factor a trinomial. 8((-1 + x)(1 + -2x)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1Subproblem 2
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 = 0.5Solution
x = {1, 0.5}
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