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Simplifying 0 = -16x2 + 64x + -28 Reorder the terms: 0 = -28 + 64x + -16x2 Solving 0 = -28 + 64x + -16x2 Solving for variable 'x'. Combine like terms: 0 + 28 = 28 28 + -64x + 16x2 = -28 + 64x + -16x2 + 28 + -64x + 16x2 Reorder the terms: 28 + -64x + 16x2 = -28 + 28 + 64x + -64x + -16x2 + 16x2 Combine like terms: -28 + 28 = 0 28 + -64x + 16x2 = 0 + 64x + -64x + -16x2 + 16x2 28 + -64x + 16x2 = 64x + -64x + -16x2 + 16x2 Combine like terms: 64x + -64x = 0 28 + -64x + 16x2 = 0 + -16x2 + 16x2 28 + -64x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 28 + -64x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(7 + -16x + 4x2) = 0 Factor a trinomial. 4((1 + -2x)(7 + -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 '(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 = 3.5Solution
x = {0.5, 3.5}
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