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Simplifying 2(x + 9)(x + -4) + -1x(x + 9) = 138 Reorder the terms: 2(9 + x)(x + -4) + -1x(x + 9) = 138 Reorder the terms: 2(9 + x)(-4 + x) + -1x(x + 9) = 138 Multiply (9 + x) * (-4 + x) 2(9(-4 + x) + x(-4 + x)) + -1x(x + 9) = 138 2((-4 * 9 + x * 9) + x(-4 + x)) + -1x(x + 9) = 138 2((-36 + 9x) + x(-4 + x)) + -1x(x + 9) = 138 2(-36 + 9x + (-4 * x + x * x)) + -1x(x + 9) = 138 2(-36 + 9x + (-4x + x2)) + -1x(x + 9) = 138 Combine like terms: 9x + -4x = 5x 2(-36 + 5x + x2) + -1x(x + 9) = 138 (-36 * 2 + 5x * 2 + x2 * 2) + -1x(x + 9) = 138 (-72 + 10x + 2x2) + -1x(x + 9) = 138 Reorder the terms: -72 + 10x + 2x2 + -1x(9 + x) = 138 -72 + 10x + 2x2 + (9 * -1x + x * -1x) = 138 -72 + 10x + 2x2 + (-9x + -1x2) = 138 Reorder the terms: -72 + 10x + -9x + 2x2 + -1x2 = 138 Combine like terms: 10x + -9x = 1x -72 + 1x + 2x2 + -1x2 = 138 Combine like terms: 2x2 + -1x2 = 1x2 -72 + 1x + 1x2 = 138 Solving -72 + 1x + 1x2 = 138 Solving for variable 'x'. Reorder the terms: -72 + -138 + 1x + 1x2 = 138 + -138 Combine like terms: -72 + -138 = -210 -210 + 1x + 1x2 = 138 + -138 Combine like terms: 138 + -138 = 0 -210 + 1x + 1x2 = 0 Factor a trinomial. (-15 + -1x)(14 + -1x) = 0Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve: Simplifying -15 + -1x = 0 Solving -15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1x = 0 + 15 -1x = 0 + 15 Combine like terms: 0 + 15 = 15 -1x = 15 Divide each side by '-1'. x = -15 Simplifying x = -15Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve: Simplifying 14 + -1x = 0 Solving 14 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1x = 0 + -14 -1x = 0 + -14 Combine like terms: 0 + -14 = -14 -1x = -14 Divide each side by '-1'. x = 14 Simplifying x = 14Solution
x = {-15, 14}
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