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Simplifying (375 + x)(240 + x) + -180000 = 0 Multiply (375 + x) * (240 + x) (375(240 + x) + x(240 + x)) + -180000 = 0 ((240 * 375 + x * 375) + x(240 + x)) + -180000 = 0 ((90000 + 375x) + x(240 + x)) + -180000 = 0 (90000 + 375x + (240 * x + x * x)) + -180000 = 0 (90000 + 375x + (240x + x2)) + -180000 = 0 Combine like terms: 375x + 240x = 615x (90000 + 615x + x2) + -180000 = 0 Reorder the terms: 90000 + -180000 + 615x + x2 = 0 Combine like terms: 90000 + -180000 = -90000 -90000 + 615x + x2 = 0 Solving -90000 + 615x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '90000' to each side of the equation. -90000 + 615x + 90000 + x2 = 0 + 90000 Reorder the terms: -90000 + 90000 + 615x + x2 = 0 + 90000 Combine like terms: -90000 + 90000 = 0 0 + 615x + x2 = 0 + 90000 615x + x2 = 0 + 90000 Combine like terms: 0 + 90000 = 90000 615x + x2 = 90000 The x term is 615x. Take half its coefficient (307.5). Square it (94556.25) and add it to both sides. Add '94556.25' to each side of the equation. 615x + 94556.25 + x2 = 90000 + 94556.25 Reorder the terms: 94556.25 + 615x + x2 = 90000 + 94556.25 Combine like terms: 90000 + 94556.25 = 184556.25 94556.25 + 615x + x2 = 184556.25 Factor a perfect square on the left side: (x + 307.5)(x + 307.5) = 184556.25 Calculate the square root of the right side: 429.600104749 Break this problem into two subproblems by setting (x + 307.5) equal to 429.600104749 and -429.600104749.Subproblem 1
x + 307.5 = 429.600104749 Simplifying x + 307.5 = 429.600104749 Reorder the terms: 307.5 + x = 429.600104749 Solving 307.5 + x = 429.600104749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-307.5' to each side of the equation. 307.5 + -307.5 + x = 429.600104749 + -307.5 Combine like terms: 307.5 + -307.5 = 0.0 0.0 + x = 429.600104749 + -307.5 x = 429.600104749 + -307.5 Combine like terms: 429.600104749 + -307.5 = 122.100104749 x = 122.100104749 Simplifying x = 122.100104749Subproblem 2
x + 307.5 = -429.600104749 Simplifying x + 307.5 = -429.600104749 Reorder the terms: 307.5 + x = -429.600104749 Solving 307.5 + x = -429.600104749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-307.5' to each side of the equation. 307.5 + -307.5 + x = -429.600104749 + -307.5 Combine like terms: 307.5 + -307.5 = 0.0 0.0 + x = -429.600104749 + -307.5 x = -429.600104749 + -307.5 Combine like terms: -429.600104749 + -307.5 = -737.100104749 x = -737.100104749 Simplifying x = -737.100104749Solution
The solution to the problem is based on the solutions from the subproblems. x = {122.100104749, -737.100104749}
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