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Simplifying x2 + -2x + 12 + 43 = 90 Reorder the terms: 12 + 43 + -2x + x2 = 90 Combine like terms: 12 + 43 = 55 55 + -2x + x2 = 90 Solving 55 + -2x + x2 = 90 Solving for variable 'x'. Reorder the terms: 55 + -90 + -2x + x2 = 90 + -90 Combine like terms: 55 + -90 = -35 -35 + -2x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -35 + -2x + x2 = 0 Factor a trinomial. (-5 + -1x)(7 + -1x) = 0Subproblem 1
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 = -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 = {-5, 7}
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