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Simplifying 7 = -16x2 + 16x + 3 Reorder the terms: 7 = 3 + 16x + -16x2 Solving 7 = 3 + 16x + -16x2 Solving for variable 'x'. Combine like terms: 7 + -3 = 4 4 + -16x + 16x2 = 3 + 16x + -16x2 + -3 + -16x + 16x2 Reorder the terms: 4 + -16x + 16x2 = 3 + -3 + 16x + -16x + -16x2 + 16x2 Combine like terms: 3 + -3 = 0 4 + -16x + 16x2 = 0 + 16x + -16x + -16x2 + 16x2 4 + -16x + 16x2 = 16x + -16x + -16x2 + 16x2 Combine like terms: 16x + -16x = 0 4 + -16x + 16x2 = 0 + -16x2 + 16x2 4 + -16x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 4 + -16x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(1 + -4x + 4x2) = 0 Factor a trinomial. 4((1 + -2x)(1 + -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 '(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 = {0.5, 0.5}
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