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Simplifying (20 + x)(30 + x) = 1200 Multiply (20 + x) * (30 + x) (20(30 + x) + x(30 + x)) = 1200 ((30 * 20 + x * 20) + x(30 + x)) = 1200 ((600 + 20x) + x(30 + x)) = 1200 (600 + 20x + (30 * x + x * x)) = 1200 (600 + 20x + (30x + x2)) = 1200 Combine like terms: 20x + 30x = 50x (600 + 50x + x2) = 1200 Solving 600 + 50x + x2 = 1200 Solving for variable 'x'. Reorder the terms: 600 + -1200 + 50x + x2 = 1200 + -1200 Combine like terms: 600 + -1200 = -600 -600 + 50x + x2 = 1200 + -1200 Combine like terms: 1200 + -1200 = 0 -600 + 50x + x2 = 0 Factor a trinomial. (-60 + -1x)(10 + -1x) = 0Subproblem 1
Set the factor '(-60 + -1x)' equal to zero and attempt to solve: Simplifying -60 + -1x = 0 Solving -60 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + -1x = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -1x = 0 + 60 -1x = 0 + 60 Combine like terms: 0 + 60 = 60 -1x = 60 Divide each side by '-1'. x = -60 Simplifying x = -60Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {-60, 10}
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