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Simplifying 26 = -2x2 + 28x Reorder the terms: 26 = 28x + -2x2 Solving 26 = 28x + -2x2 Solving for variable 'x'. Reorder the terms: 26 + -28x + 2x2 = 28x + -28x + -2x2 + 2x2 Combine like terms: 28x + -28x = 0 26 + -28x + 2x2 = 0 + -2x2 + 2x2 26 + -28x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 26 + -28x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(13 + -14x + x2) = 0 Factor a trinomial. 2((1 + -1x)(13 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve: Simplifying 13 + -1x = 0 Solving 13 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1x = 0 + -13 -1x = 0 + -13 Combine like terms: 0 + -13 = -13 -1x = -13 Divide each side by '-1'. x = 13 Simplifying x = 13Solution
x = {1, 13}
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