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Simplifying (x + 5)(x + 2) + -40 = 0 Reorder the terms: (5 + x)(x + 2) + -40 = 0 Reorder the terms: (5 + x)(2 + x) + -40 = 0 Multiply (5 + x) * (2 + x) (5(2 + x) + x(2 + x)) + -40 = 0 ((2 * 5 + x * 5) + x(2 + x)) + -40 = 0 ((10 + 5x) + x(2 + x)) + -40 = 0 (10 + 5x + (2 * x + x * x)) + -40 = 0 (10 + 5x + (2x + x2)) + -40 = 0 Combine like terms: 5x + 2x = 7x (10 + 7x + x2) + -40 = 0 Reorder the terms: 10 + -40 + 7x + x2 = 0 Combine like terms: 10 + -40 = -30 -30 + 7x + x2 = 0 Solving -30 + 7x + x2 = 0 Solving for variable 'x'. Factor a trinomial. (-10 + -1x)(3 + -1x) = 0Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve: Simplifying -10 + -1x = 0 Solving -10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1x = 0 + 10 -1x = 0 + 10 Combine like terms: 0 + 10 = 10 -1x = 10 Divide each side by '-1'. x = -10 Simplifying x = -10Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-10, 3}
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