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Simplifying (x + -1)(5 + x) = 40 Reorder the terms: (-1 + x)(5 + x) = 40 Multiply (-1 + x) * (5 + x) (-1(5 + x) + x(5 + x)) = 40 ((5 * -1 + x * -1) + x(5 + x)) = 40 ((-5 + -1x) + x(5 + x)) = 40 (-5 + -1x + (5 * x + x * x)) = 40 (-5 + -1x + (5x + x2)) = 40 Combine like terms: -1x + 5x = 4x (-5 + 4x + x2) = 40 Solving -5 + 4x + x2 = 40 Solving for variable 'x'. Reorder the terms: -5 + -40 + 4x + x2 = 40 + -40 Combine like terms: -5 + -40 = -45 -45 + 4x + x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -45 + 4x + x2 = 0 Factor a trinomial. (-9 + -1x)(5 + -1x) = 0Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9Subproblem 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 = {-9, 5}
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