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Simplifying -16x2 + 96x + 12 = 152 Reorder the terms: 12 + 96x + -16x2 = 152 Solving 12 + 96x + -16x2 = 152 Solving for variable 'x'. Reorder the terms: 12 + -152 + 96x + -16x2 = 152 + -152 Combine like terms: 12 + -152 = -140 -140 + 96x + -16x2 = 152 + -152 Combine like terms: 152 + -152 = 0 -140 + 96x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-35 + 24x + -4x2) = 0 Factor a trinomial. 4((-7 + 2x)(5 + -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 '(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 = {3.5, 2.5}
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