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Simplifying (5 + x)(3 + x) = 48 Multiply (5 + x) * (3 + x) (5(3 + x) + x(3 + x)) = 48 ((3 * 5 + x * 5) + x(3 + x)) = 48 ((15 + 5x) + x(3 + x)) = 48 (15 + 5x + (3 * x + x * x)) = 48 (15 + 5x + (3x + x2)) = 48 Combine like terms: 5x + 3x = 8x (15 + 8x + x2) = 48 Solving 15 + 8x + x2 = 48 Solving for variable 'x'. Reorder the terms: 15 + -48 + 8x + x2 = 48 + -48 Combine like terms: 15 + -48 = -33 -33 + 8x + x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -33 + 8x + x2 = 0 Factor a trinomial. (-11 + -1x)(3 + -1x) = 0Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve: Simplifying -11 + -1x = 0 Solving -11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -1x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1x = 0 + 11 -1x = 0 + 11 Combine like terms: 0 + 11 = 11 -1x = 11 Divide each side by '-1'. x = -11 Simplifying x = -11Subproblem 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 = {-11, 3}
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