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Simplifying (x + 2)(x + 5) = 70 Reorder the terms: (2 + x)(x + 5) = 70 Reorder the terms: (2 + x)(5 + x) = 70 Multiply (2 + x) * (5 + x) (2(5 + x) + x(5 + x)) = 70 ((5 * 2 + x * 2) + x(5 + x)) = 70 ((10 + 2x) + x(5 + x)) = 70 (10 + 2x + (5 * x + x * x)) = 70 (10 + 2x + (5x + x2)) = 70 Combine like terms: 2x + 5x = 7x (10 + 7x + x2) = 70 Solving 10 + 7x + x2 = 70 Solving for variable 'x'. Reorder the terms: 10 + -70 + 7x + x2 = 70 + -70 Combine like terms: 10 + -70 = -60 -60 + 7x + x2 = 70 + -70 Combine like terms: 70 + -70 = 0 -60 + 7x + x2 = 0 Factor a trinomial. (-12 + -1x)(5 + -1x) = 0Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve: Simplifying -12 + -1x = 0 Solving -12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1x = 0 + 12 -1x = 0 + 12 Combine like terms: 0 + 12 = 12 -1x = 12 Divide each side by '-1'. x = -12 Simplifying x = -12Subproblem 2
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 = 5Solution
x = {-12, 5}
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