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Simplifying (4 + x)(5 + x) = 56 Multiply (4 + x) * (5 + x) (4(5 + x) + x(5 + x)) = 56 ((5 * 4 + x * 4) + x(5 + x)) = 56 ((20 + 4x) + x(5 + x)) = 56 (20 + 4x + (5 * x + x * x)) = 56 (20 + 4x + (5x + x2)) = 56 Combine like terms: 4x + 5x = 9x (20 + 9x + x2) = 56 Solving 20 + 9x + x2 = 56 Solving for variable 'x'. Reorder the terms: 20 + -56 + 9x + x2 = 56 + -56 Combine like terms: 20 + -56 = -36 -36 + 9x + x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -36 + 9x + x2 = 0 Factor a trinomial. (-12 + -1x)(3 + -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 '(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 = {-12, 3}
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