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Simplifying (x + 5)(x + 10) = 126 Reorder the terms: (5 + x)(x + 10) = 126 Reorder the terms: (5 + x)(10 + x) = 126 Multiply (5 + x) * (10 + x) (5(10 + x) + x(10 + x)) = 126 ((10 * 5 + x * 5) + x(10 + x)) = 126 ((50 + 5x) + x(10 + x)) = 126 (50 + 5x + (10 * x + x * x)) = 126 (50 + 5x + (10x + x2)) = 126 Combine like terms: 5x + 10x = 15x (50 + 15x + x2) = 126 Solving 50 + 15x + x2 = 126 Solving for variable 'x'. Reorder the terms: 50 + -126 + 15x + x2 = 126 + -126 Combine like terms: 50 + -126 = -76 -76 + 15x + x2 = 126 + -126 Combine like terms: 126 + -126 = 0 -76 + 15x + x2 = 0 Factor a trinomial. (-19 + -1x)(4 + -1x) = 0Subproblem 1
Set the factor '(-19 + -1x)' equal to zero and attempt to solve: Simplifying -19 + -1x = 0 Solving -19 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + -1x = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -1x = 0 + 19 -1x = 0 + 19 Combine like terms: 0 + 19 = 19 -1x = 19 Divide each side by '-1'. x = -19 Simplifying x = -19Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-19, 4}
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