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Simplifying -16x2 + 64x + 12 = 40 Reorder the terms: 12 + 64x + -16x2 = 40 Solving 12 + 64x + -16x2 = 40 Solving for variable 'x'. Reorder the terms: 12 + -40 + 64x + -16x2 = 40 + -40 Combine like terms: 12 + -40 = -28 -28 + 64x + -16x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -28 + 64x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-7 + 16x + -4x2) = 0 Factor a trinomial. 4((-7 + 2x)(1 + -2x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-7 + 2x)' equal to zero and attempt to solve: Simplifying -7 + 2x = 0 Solving -7 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 2x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2x = 0 + 7 2x = 0 + 7 Combine like terms: 0 + 7 = 7 2x = 7 Divide each side by '2'. x = 3.5 Simplifying x = 3.5Subproblem 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 = {3.5, 0.5}
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