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Simplifying 130500 = (240 + x)(375 + x) Multiply (240 + x) * (375 + x) 130500 = (240(375 + x) + x(375 + x)) 130500 = ((375 * 240 + x * 240) + x(375 + x)) 130500 = ((90000 + 240x) + x(375 + x)) 130500 = (90000 + 240x + (375 * x + x * x)) 130500 = (90000 + 240x + (375x + x2)) Combine like terms: 240x + 375x = 615x 130500 = (90000 + 615x + x2) Solving 130500 = 90000 + 615x + x2 Solving for variable 'x'. Combine like terms: 130500 + -90000 = 40500 40500 + -615x + -1x2 = 90000 + 615x + x2 + -90000 + -615x + -1x2 Reorder the terms: 40500 + -615x + -1x2 = 90000 + -90000 + 615x + -615x + x2 + -1x2 Combine like terms: 90000 + -90000 = 0 40500 + -615x + -1x2 = 0 + 615x + -615x + x2 + -1x2 40500 + -615x + -1x2 = 615x + -615x + x2 + -1x2 Combine like terms: 615x + -615x = 0 40500 + -615x + -1x2 = 0 + x2 + -1x2 40500 + -615x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 40500 + -615x + -1x2 = 0 Factor a trinomial. (60 + -1x)(675 + x) = 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 '(675 + x)' equal to zero and attempt to solve: Simplifying 675 + x = 0 Solving 675 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-675' to each side of the equation. 675 + -675 + x = 0 + -675 Combine like terms: 675 + -675 = 0 0 + x = 0 + -675 x = 0 + -675 Combine like terms: 0 + -675 = -675 x = -675 Simplifying x = -675Solution
x = {60, -675}
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