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Simplifying 300 = (x + 10)((x + 5) + 10) Reorder the terms: 300 = (10 + x)((x + 5) + 10) Reorder the terms: 300 = (10 + x)((5 + x) + 10) Remove parenthesis around (5 + x) 300 = (10 + x)(5 + x + 10) Reorder the terms: 300 = (10 + x)(5 + 10 + x) Combine like terms: 5 + 10 = 15 300 = (10 + x)(15 + x) Multiply (10 + x) * (15 + x) 300 = (10(15 + x) + x(15 + x)) 300 = ((15 * 10 + x * 10) + x(15 + x)) 300 = ((150 + 10x) + x(15 + x)) 300 = (150 + 10x + (15 * x + x * x)) 300 = (150 + 10x + (15x + x2)) Combine like terms: 10x + 15x = 25x 300 = (150 + 25x + x2) Solving 300 = 150 + 25x + x2 Solving for variable 'x'. Combine like terms: 300 + -150 = 150 150 + -25x + -1x2 = 150 + 25x + x2 + -150 + -25x + -1x2 Reorder the terms: 150 + -25x + -1x2 = 150 + -150 + 25x + -25x + x2 + -1x2 Combine like terms: 150 + -150 = 0 150 + -25x + -1x2 = 0 + 25x + -25x + x2 + -1x2 150 + -25x + -1x2 = 25x + -25x + x2 + -1x2 Combine like terms: 25x + -25x = 0 150 + -25x + -1x2 = 0 + x2 + -1x2 150 + -25x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 150 + -25x + -1x2 = 0 Factor a trinomial. (5 + -1x)(30 + x) = 0Subproblem 1
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 = 5Subproblem 2
Set the factor '(30 + x)' equal to zero and attempt to solve: Simplifying 30 + x = 0 Solving 30 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = 0 + -30 Combine like terms: 30 + -30 = 0 0 + x = 0 + -30 x = 0 + -30 Combine like terms: 0 + -30 = -30 x = -30 Simplifying x = -30Solution
x = {5, -30}
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