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Simplifying x2 + 540x + -72000 = 0 Reorder the terms: -72000 + 540x + x2 = 0 Solving -72000 + 540x + 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 + 540x + 72000 + x2 = 0 + 72000 Reorder the terms: -72000 + 72000 + 540x + x2 = 0 + 72000 Combine like terms: -72000 + 72000 = 0 0 + 540x + x2 = 0 + 72000 540x + x2 = 0 + 72000 Combine like terms: 0 + 72000 = 72000 540x + x2 = 72000 The x term is 540x. Take half its coefficient (270). Square it (72900) and add it to both sides. Add '72900' to each side of the equation. 540x + 72900 + x2 = 72000 + 72900 Reorder the terms: 72900 + 540x + x2 = 72000 + 72900 Combine like terms: 72000 + 72900 = 144900 72900 + 540x + x2 = 144900 Factor a perfect square on the left side: (x + 270)(x + 270) = 144900 Calculate the square root of the right side: 380.657326213 Break this problem into two subproblems by setting (x + 270) equal to 380.657326213 and -380.657326213.Subproblem 1
x + 270 = 380.657326213 Simplifying x + 270 = 380.657326213 Reorder the terms: 270 + x = 380.657326213 Solving 270 + x = 380.657326213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-270' to each side of the equation. 270 + -270 + x = 380.657326213 + -270 Combine like terms: 270 + -270 = 0 0 + x = 380.657326213 + -270 x = 380.657326213 + -270 Combine like terms: 380.657326213 + -270 = 110.657326213 x = 110.657326213 Simplifying x = 110.657326213Subproblem 2
x + 270 = -380.657326213 Simplifying x + 270 = -380.657326213 Reorder the terms: 270 + x = -380.657326213 Solving 270 + x = -380.657326213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-270' to each side of the equation. 270 + -270 + x = -380.657326213 + -270 Combine like terms: 270 + -270 = 0 0 + x = -380.657326213 + -270 x = -380.657326213 + -270 Combine like terms: -380.657326213 + -270 = -650.657326213 x = -650.657326213 Simplifying x = -650.657326213Solution
The solution to the problem is based on the solutions from the subproblems. x = {110.657326213, -650.657326213}
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