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Simplifying 2x + -18 = (2x + -18)(2x + 6) Reorder the terms: -18 + 2x = (2x + -18)(2x + 6) Reorder the terms: -18 + 2x = (-18 + 2x)(2x + 6) Reorder the terms: -18 + 2x = (-18 + 2x)(6 + 2x) Multiply (-18 + 2x) * (6 + 2x) -18 + 2x = (-18(6 + 2x) + 2x * (6 + 2x)) -18 + 2x = ((6 * -18 + 2x * -18) + 2x * (6 + 2x)) -18 + 2x = ((-108 + -36x) + 2x * (6 + 2x)) -18 + 2x = (-108 + -36x + (6 * 2x + 2x * 2x)) -18 + 2x = (-108 + -36x + (12x + 4x2)) Combine like terms: -36x + 12x = -24x -18 + 2x = (-108 + -24x + 4x2) Solving -18 + 2x = -108 + -24x + 4x2 Solving for variable 'x'. Reorder the terms: -18 + 108 + 2x + 24x + -4x2 = -108 + -24x + 4x2 + 108 + 24x + -4x2 Combine like terms: -18 + 108 = 90 90 + 2x + 24x + -4x2 = -108 + -24x + 4x2 + 108 + 24x + -4x2 Combine like terms: 2x + 24x = 26x 90 + 26x + -4x2 = -108 + -24x + 4x2 + 108 + 24x + -4x2 Reorder the terms: 90 + 26x + -4x2 = -108 + 108 + -24x + 24x + 4x2 + -4x2 Combine like terms: -108 + 108 = 0 90 + 26x + -4x2 = 0 + -24x + 24x + 4x2 + -4x2 90 + 26x + -4x2 = -24x + 24x + 4x2 + -4x2 Combine like terms: -24x + 24x = 0 90 + 26x + -4x2 = 0 + 4x2 + -4x2 90 + 26x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 90 + 26x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(45 + 13x + -2x2) = 0 Factor a trinomial. 2((9 + -1x)(5 + 2x)) = 0 Ignore the factor 2.Subproblem 1
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 = 9Subproblem 2
Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 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 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5Solution
x = {9, -2.5}
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