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Simplifying x(x + 2) = 3(x + 4) + 18 Reorder the terms: x(2 + x) = 3(x + 4) + 18 (2 * x + x * x) = 3(x + 4) + 18 (2x + x2) = 3(x + 4) + 18 Reorder the terms: 2x + x2 = 3(4 + x) + 18 2x + x2 = (4 * 3 + x * 3) + 18 2x + x2 = (12 + 3x) + 18 Reorder the terms: 2x + x2 = 12 + 18 + 3x Combine like terms: 12 + 18 = 30 2x + x2 = 30 + 3x Solving 2x + x2 = 30 + 3x Solving for variable 'x'. Reorder the terms: -30 + 2x + -3x + x2 = 30 + 3x + -30 + -3x Combine like terms: 2x + -3x = -1x -30 + -1x + x2 = 30 + 3x + -30 + -3x Reorder the terms: -30 + -1x + x2 = 30 + -30 + 3x + -3x Combine like terms: 30 + -30 = 0 -30 + -1x + x2 = 0 + 3x + -3x -30 + -1x + x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -30 + -1x + x2 = 0 Factor a trinomial. (-5 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-5, 6}
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