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Simplifying x2 + 615x + -72000 = 0 Reorder the terms: -72000 + 615x + x2 = 0 Solving -72000 + 615x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '72000' to each side of the equation. -72000 + 615x + 72000 + x2 = 0 + 72000 Reorder the terms: -72000 + 72000 + 615x + x2 = 0 + 72000 Combine like terms: -72000 + 72000 = 0 0 + 615x + x2 = 0 + 72000 615x + x2 = 0 + 72000 Combine like terms: 0 + 72000 = 72000 615x + x2 = 72000 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 = 72000 + 94556.25 Reorder the terms: 94556.25 + 615x + x2 = 72000 + 94556.25 Combine like terms: 72000 + 94556.25 = 166556.25 94556.25 + 615x + x2 = 166556.25 Factor a perfect square on the left side: (x + 307.5)(x + 307.5) = 166556.25 Calculate the square root of the right side: 408.113035812 Break this problem into two subproblems by setting (x + 307.5) equal to 408.113035812 and -408.113035812.Subproblem 1
x + 307.5 = 408.113035812 Simplifying x + 307.5 = 408.113035812 Reorder the terms: 307.5 + x = 408.113035812 Solving 307.5 + x = 408.113035812 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 = 408.113035812 + -307.5 Combine like terms: 307.5 + -307.5 = 0.0 0.0 + x = 408.113035812 + -307.5 x = 408.113035812 + -307.5 Combine like terms: 408.113035812 + -307.5 = 100.613035812 x = 100.613035812 Simplifying x = 100.613035812Subproblem 2
x + 307.5 = -408.113035812 Simplifying x + 307.5 = -408.113035812 Reorder the terms: 307.5 + x = -408.113035812 Solving 307.5 + x = -408.113035812 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 = -408.113035812 + -307.5 Combine like terms: 307.5 + -307.5 = 0.0 0.0 + x = -408.113035812 + -307.5 x = -408.113035812 + -307.5 Combine like terms: -408.113035812 + -307.5 = -715.613035812 x = -715.613035812 Simplifying x = -715.613035812Solution
The solution to the problem is based on the solutions from the subproblems. x = {100.613035812, -715.613035812}
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