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Simplifying (x + 40)(x + 90) = 600 Reorder the terms: (40 + x)(x + 90) = 600 Reorder the terms: (40 + x)(90 + x) = 600 Multiply (40 + x) * (90 + x) (40(90 + x) + x(90 + x)) = 600 ((90 * 40 + x * 40) + x(90 + x)) = 600 ((3600 + 40x) + x(90 + x)) = 600 (3600 + 40x + (90 * x + x * x)) = 600 (3600 + 40x + (90x + x2)) = 600 Combine like terms: 40x + 90x = 130x (3600 + 130x + x2) = 600 Solving 3600 + 130x + x2 = 600 Solving for variable 'x'. Reorder the terms: 3600 + -600 + 130x + x2 = 600 + -600 Combine like terms: 3600 + -600 = 3000 3000 + 130x + x2 = 600 + -600 Combine like terms: 600 + -600 = 0 3000 + 130x + x2 = 0 Factor a trinomial. (100 + x)(30 + x) = 0Subproblem 1
Set the factor '(100 + x)' equal to zero and attempt to solve: Simplifying 100 + x = 0 Solving 100 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + x = 0 + -100 Combine like terms: 100 + -100 = 0 0 + x = 0 + -100 x = 0 + -100 Combine like terms: 0 + -100 = -100 x = -100 Simplifying x = -100Subproblem 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 = {-100, -30}
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