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Simplifying 8x + -9 = x2 + x + 3 Reorder the terms: -9 + 8x = x2 + x + 3 Reorder the terms: -9 + 8x = 3 + x + x2 Solving -9 + 8x = 3 + x + x2 Solving for variable 'x'. Reorder the terms: -9 + -3 + 8x + -1x + -1x2 = 3 + x + x2 + -3 + -1x + -1x2 Combine like terms: -9 + -3 = -12 -12 + 8x + -1x + -1x2 = 3 + x + x2 + -3 + -1x + -1x2 Combine like terms: 8x + -1x = 7x -12 + 7x + -1x2 = 3 + x + x2 + -3 + -1x + -1x2 Reorder the terms: -12 + 7x + -1x2 = 3 + -3 + x + -1x + x2 + -1x2 Combine like terms: 3 + -3 = 0 -12 + 7x + -1x2 = 0 + x + -1x + x2 + -1x2 -12 + 7x + -1x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 -12 + 7x + -1x2 = 0 + x2 + -1x2 -12 + 7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -12 + 7x + -1x2 = 0 Factor a trinomial. (-4 + x)(3 + -1x) = 0Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 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 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Simplifying x = 4Subproblem 2
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 = 3Solution
x = {4, 3}
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