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Simplifying 62 = -16x2 + 64x + 2 Reorder the terms: 62 = 2 + 64x + -16x2 Solving 62 = 2 + 64x + -16x2 Solving for variable 'x'. Combine like terms: 62 + -2 = 60 60 + -64x + 16x2 = 2 + 64x + -16x2 + -2 + -64x + 16x2 Reorder the terms: 60 + -64x + 16x2 = 2 + -2 + 64x + -64x + -16x2 + 16x2 Combine like terms: 2 + -2 = 0 60 + -64x + 16x2 = 0 + 64x + -64x + -16x2 + 16x2 60 + -64x + 16x2 = 64x + -64x + -16x2 + 16x2 Combine like terms: 64x + -64x = 0 60 + -64x + 16x2 = 0 + -16x2 + 16x2 60 + -64x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 60 + -64x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(15 + -16x + 4x2) = 0 Factor a trinomial. 4((3 + -2x)(5 + -2x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Subproblem 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 = {1.5, 2.5}
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