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Simplifying 0 = 2x2 + -26x + 24 Reorder the terms: 0 = 24 + -26x + 2x2 Solving 0 = 24 + -26x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -24 = -24 -24 + 26x + -2x2 = 24 + -26x + 2x2 + -24 + 26x + -2x2 Reorder the terms: -24 + 26x + -2x2 = 24 + -24 + -26x + 26x + 2x2 + -2x2 Combine like terms: 24 + -24 = 0 -24 + 26x + -2x2 = 0 + -26x + 26x + 2x2 + -2x2 -24 + 26x + -2x2 = -26x + 26x + 2x2 + -2x2 Combine like terms: -26x + 26x = 0 -24 + 26x + -2x2 = 0 + 2x2 + -2x2 -24 + 26x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -24 + 26x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 13x + -1x2) = 0 Factor a trinomial. 2((-12 + x)(1 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + x)' equal to zero and attempt to solve: Simplifying -12 + x = 0 Solving -12 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + x = 0 + 12 x = 0 + 12 Combine like terms: 0 + 12 = 12 x = 12 Simplifying x = 12Subproblem 2
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 = 1Solution
x = {12, 1}
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