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Simplifying 12x + 5 = -26x2 + x + 20 Reorder the terms: 5 + 12x = -26x2 + x + 20 Reorder the terms: 5 + 12x = 20 + x + -26x2 Solving 5 + 12x = 20 + x + -26x2 Solving for variable 'x'. Reorder the terms: 5 + -20 + 12x + -1x + 26x2 = 20 + x + -26x2 + -20 + -1x + 26x2 Combine like terms: 5 + -20 = -15 -15 + 12x + -1x + 26x2 = 20 + x + -26x2 + -20 + -1x + 26x2 Combine like terms: 12x + -1x = 11x -15 + 11x + 26x2 = 20 + x + -26x2 + -20 + -1x + 26x2 Reorder the terms: -15 + 11x + 26x2 = 20 + -20 + x + -1x + -26x2 + 26x2 Combine like terms: 20 + -20 = 0 -15 + 11x + 26x2 = 0 + x + -1x + -26x2 + 26x2 -15 + 11x + 26x2 = x + -1x + -26x2 + 26x2 Combine like terms: x + -1x = 0 -15 + 11x + 26x2 = 0 + -26x2 + 26x2 -15 + 11x + 26x2 = -26x2 + 26x2 Combine like terms: -26x2 + 26x2 = 0 -15 + 11x + 26x2 = 0 Factor a trinomial. (-1 + -1x)(15 + -26x) = 0Subproblem 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 '(15 + -26x)' equal to zero and attempt to solve: Simplifying 15 + -26x = 0 Solving 15 + -26x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -26x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -26x = 0 + -15 -26x = 0 + -15 Combine like terms: 0 + -15 = -15 -26x = -15 Divide each side by '-26'. x = 0.5769230769 Simplifying x = 0.5769230769Solution
x = {-1, 0.5769230769}
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