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Simplifying (x + 5)(x + -2) = 8 Reorder the terms: (5 + x)(x + -2) = 8 Reorder the terms: (5 + x)(-2 + x) = 8 Multiply (5 + x) * (-2 + x) (5(-2 + x) + x(-2 + x)) = 8 ((-2 * 5 + x * 5) + x(-2 + x)) = 8 ((-10 + 5x) + x(-2 + x)) = 8 (-10 + 5x + (-2 * x + x * x)) = 8 (-10 + 5x + (-2x + x2)) = 8 Combine like terms: 5x + -2x = 3x (-10 + 3x + x2) = 8 Solving -10 + 3x + x2 = 8 Solving for variable 'x'. Reorder the terms: -10 + -8 + 3x + x2 = 8 + -8 Combine like terms: -10 + -8 = -18 -18 + 3x + x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -18 + 3x + x2 = 0 Factor a trinomial. (-6 + -1x)(3 + -1x) = 0Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 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 = {-6, 3}
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