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Simplifying x2 + -19x + 32 = -7x + 5 Reorder the terms: 32 + -19x + x2 = -7x + 5 Reorder the terms: 32 + -19x + x2 = 5 + -7x Solving 32 + -19x + x2 = 5 + -7x Solving for variable 'x'. Reorder the terms: 32 + -5 + -19x + 7x + x2 = 5 + -7x + -5 + 7x Combine like terms: 32 + -5 = 27 27 + -19x + 7x + x2 = 5 + -7x + -5 + 7x Combine like terms: -19x + 7x = -12x 27 + -12x + x2 = 5 + -7x + -5 + 7x Reorder the terms: 27 + -12x + x2 = 5 + -5 + -7x + 7x Combine like terms: 5 + -5 = 0 27 + -12x + x2 = 0 + -7x + 7x 27 + -12x + x2 = -7x + 7x Combine like terms: -7x + 7x = 0 27 + -12x + x2 = 0 Factor a trinomial. (3 + -1x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {3, 9}
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