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Simplifying x2 + -48x + -540 = 0 Reorder the terms: -540 + -48x + x2 = 0 Solving -540 + -48x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '540' to each side of the equation. -540 + -48x + 540 + x2 = 0 + 540 Reorder the terms: -540 + 540 + -48x + x2 = 0 + 540 Combine like terms: -540 + 540 = 0 0 + -48x + x2 = 0 + 540 -48x + x2 = 0 + 540 Combine like terms: 0 + 540 = 540 -48x + x2 = 540 The x term is -48x. Take half its coefficient (-24). Square it (576) and add it to both sides. Add '576' to each side of the equation. -48x + 576 + x2 = 540 + 576 Reorder the terms: 576 + -48x + x2 = 540 + 576 Combine like terms: 540 + 576 = 1116 576 + -48x + x2 = 1116 Factor a perfect square on the left side: (x + -24)(x + -24) = 1116 Calculate the square root of the right side: 33.406586177 Break this problem into two subproblems by setting (x + -24) equal to 33.406586177 and -33.406586177.Subproblem 1
x + -24 = 33.406586177 Simplifying x + -24 = 33.406586177 Reorder the terms: -24 + x = 33.406586177 Solving -24 + x = 33.406586177 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = 33.406586177 + 24 Combine like terms: -24 + 24 = 0 0 + x = 33.406586177 + 24 x = 33.406586177 + 24 Combine like terms: 33.406586177 + 24 = 57.406586177 x = 57.406586177 Simplifying x = 57.406586177Subproblem 2
x + -24 = -33.406586177 Simplifying x + -24 = -33.406586177 Reorder the terms: -24 + x = -33.406586177 Solving -24 + x = -33.406586177 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = -33.406586177 + 24 Combine like terms: -24 + 24 = 0 0 + x = -33.406586177 + 24 x = -33.406586177 + 24 Combine like terms: -33.406586177 + 24 = -9.406586177 x = -9.406586177 Simplifying x = -9.406586177Solution
The solution to the problem is based on the solutions from the subproblems. x = {57.406586177, -9.406586177}
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