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Simplifying (10 + x)(25 + x) = 450 Multiply (10 + x) * (25 + x) (10(25 + x) + x(25 + x)) = 450 ((25 * 10 + x * 10) + x(25 + x)) = 450 ((250 + 10x) + x(25 + x)) = 450 (250 + 10x + (25 * x + x * x)) = 450 (250 + 10x + (25x + x2)) = 450 Combine like terms: 10x + 25x = 35x (250 + 35x + x2) = 450 Solving 250 + 35x + x2 = 450 Solving for variable 'x'. Reorder the terms: 250 + -450 + 35x + x2 = 450 + -450 Combine like terms: 250 + -450 = -200 -200 + 35x + x2 = 450 + -450 Combine like terms: 450 + -450 = 0 -200 + 35x + x2 = 0 Factor a trinomial. (-40 + -1x)(5 + -1x) = 0Subproblem 1
Set the factor '(-40 + -1x)' equal to zero and attempt to solve: Simplifying -40 + -1x = 0 Solving -40 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + -1x = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -1x = 0 + 40 -1x = 0 + 40 Combine like terms: 0 + 40 = 40 -1x = 40 Divide each side by '-1'. x = -40 Simplifying x = -40Subproblem 2
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 = 5Solution
x = {-40, 5}
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