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Simplifying 0 = -2x2 + 13x + 7 Reorder the terms: 0 = 7 + 13x + -2x2 Solving 0 = 7 + 13x + -2x2 Solving for variable 'x'. Combine like terms: 0 + -7 = -7 -7 + -13x + 2x2 = 7 + 13x + -2x2 + -7 + -13x + 2x2 Reorder the terms: -7 + -13x + 2x2 = 7 + -7 + 13x + -13x + -2x2 + 2x2 Combine like terms: 7 + -7 = 0 -7 + -13x + 2x2 = 0 + 13x + -13x + -2x2 + 2x2 -7 + -13x + 2x2 = 13x + -13x + -2x2 + 2x2 Combine like terms: 13x + -13x = 0 -7 + -13x + 2x2 = 0 + -2x2 + 2x2 -7 + -13x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -7 + -13x + 2x2 = 0 Factor a trinomial. (-1 + -2x)(7 + -1x) = 0Subproblem 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 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {-0.5, 7}
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