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Simplifying 20 = -1x2 + 8x + 5 Reorder the terms: 20 = 5 + 8x + -1x2 Solving 20 = 5 + 8x + -1x2 Solving for variable 'x'. Combine like terms: 20 + -5 = 15 15 + -8x + x2 = 5 + 8x + -1x2 + -5 + -8x + x2 Reorder the terms: 15 + -8x + x2 = 5 + -5 + 8x + -8x + -1x2 + x2 Combine like terms: 5 + -5 = 0 15 + -8x + x2 = 0 + 8x + -8x + -1x2 + x2 15 + -8x + x2 = 8x + -8x + -1x2 + x2 Combine like terms: 8x + -8x = 0 15 + -8x + x2 = 0 + -1x2 + x2 15 + -8x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 15 + -8x + x2 = 0 Factor a trinomial. (3 + -1x)(5 + -1x) = 0Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {3, 5}
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