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Simplifying (x + 5)(x + 2) = 130 Reorder the terms: (5 + x)(x + 2) = 130 Reorder the terms: (5 + x)(2 + x) = 130 Multiply (5 + x) * (2 + x) (5(2 + x) + x(2 + x)) = 130 ((2 * 5 + x * 5) + x(2 + x)) = 130 ((10 + 5x) + x(2 + x)) = 130 (10 + 5x + (2 * x + x * x)) = 130 (10 + 5x + (2x + x2)) = 130 Combine like terms: 5x + 2x = 7x (10 + 7x + x2) = 130 Solving 10 + 7x + x2 = 130 Solving for variable 'x'. Reorder the terms: 10 + -130 + 7x + x2 = 130 + -130 Combine like terms: 10 + -130 = -120 -120 + 7x + x2 = 130 + -130 Combine like terms: 130 + -130 = 0 -120 + 7x + x2 = 0 Factor a trinomial. (-15 + -1x)(8 + -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 '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {-15, 8}
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