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Simplifying x(x + 2) = 8 + x + 4 Reorder the terms: x(2 + x) = 8 + x + 4 (2 * x + x * x) = 8 + x + 4 (2x + x2) = 8 + x + 4 Reorder the terms: 2x + x2 = 8 + 4 + x Combine like terms: 8 + 4 = 12 2x + x2 = 12 + x Solving 2x + x2 = 12 + x Solving for variable 'x'. Reorder the terms: -12 + 2x + -1x + x2 = 12 + x + -12 + -1x Combine like terms: 2x + -1x = 1x -12 + 1x + x2 = 12 + x + -12 + -1x Reorder the terms: -12 + 1x + x2 = 12 + -12 + x + -1x Combine like terms: 12 + -12 = 0 -12 + 1x + x2 = 0 + x + -1x -12 + 1x + x2 = x + -1x Combine like terms: x + -1x = 0 -12 + 1x + x2 = 0 Factor a trinomial. (-4 + -1x)(3 + -1x) = 0Subproblem 1
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 = -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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