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Simplifying 8 + -1x = x2 + -12x + 36 Reorder the terms: 8 + -1x = 36 + -12x + x2 Solving 8 + -1x = 36 + -12x + x2 Solving for variable 'x'. Reorder the terms: 8 + -36 + -1x + 12x + -1x2 = 36 + -12x + x2 + -36 + 12x + -1x2 Combine like terms: 8 + -36 = -28 -28 + -1x + 12x + -1x2 = 36 + -12x + x2 + -36 + 12x + -1x2 Combine like terms: -1x + 12x = 11x -28 + 11x + -1x2 = 36 + -12x + x2 + -36 + 12x + -1x2 Reorder the terms: -28 + 11x + -1x2 = 36 + -36 + -12x + 12x + x2 + -1x2 Combine like terms: 36 + -36 = 0 -28 + 11x + -1x2 = 0 + -12x + 12x + x2 + -1x2 -28 + 11x + -1x2 = -12x + 12x + x2 + -1x2 Combine like terms: -12x + 12x = 0 -28 + 11x + -1x2 = 0 + x2 + -1x2 -28 + 11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -28 + 11x + -1x2 = 0 Factor a trinomial. (-7 + x)(4 + -1x) = 0Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve: Simplifying -7 + x = 0 Solving -7 + x = 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 + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0 + 7 x = 0 + 7 Combine like terms: 0 + 7 = 7 x = 7 Simplifying x = 7Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {7, 4}
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