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Simplifying x2 + -567.5x + 460 = 0 Reorder the terms: 460 + -567.5x + x2 = 0 Solving 460 + -567.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-460' to each side of the equation. 460 + -567.5x + -460 + x2 = 0 + -460 Reorder the terms: 460 + -460 + -567.5x + x2 = 0 + -460 Combine like terms: 460 + -460 = 0 0 + -567.5x + x2 = 0 + -460 -567.5x + x2 = 0 + -460 Combine like terms: 0 + -460 = -460 -567.5x + x2 = -460 The x term is -567.5x. Take half its coefficient (-283.75). Square it (80514.0625) and add it to both sides. Add '80514.0625' to each side of the equation. -567.5x + 80514.0625 + x2 = -460 + 80514.0625 Reorder the terms: 80514.0625 + -567.5x + x2 = -460 + 80514.0625 Combine like terms: -460 + 80514.0625 = 80054.0625 80514.0625 + -567.5x + x2 = 80054.0625 Factor a perfect square on the left side: (x + -283.75)(x + -283.75) = 80054.0625 Calculate the square root of the right side: 282.938266235 Break this problem into two subproblems by setting (x + -283.75) equal to 282.938266235 and -282.938266235.Subproblem 1
x + -283.75 = 282.938266235 Simplifying x + -283.75 = 282.938266235 Reorder the terms: -283.75 + x = 282.938266235 Solving -283.75 + x = 282.938266235 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '283.75' to each side of the equation. -283.75 + 283.75 + x = 282.938266235 + 283.75 Combine like terms: -283.75 + 283.75 = 0.00 0.00 + x = 282.938266235 + 283.75 x = 282.938266235 + 283.75 Combine like terms: 282.938266235 + 283.75 = 566.688266235 x = 566.688266235 Simplifying x = 566.688266235Subproblem 2
x + -283.75 = -282.938266235 Simplifying x + -283.75 = -282.938266235 Reorder the terms: -283.75 + x = -282.938266235 Solving -283.75 + x = -282.938266235 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '283.75' to each side of the equation. -283.75 + 283.75 + x = -282.938266235 + 283.75 Combine like terms: -283.75 + 283.75 = 0.00 0.00 + x = -282.938266235 + 283.75 x = -282.938266235 + 283.75 Combine like terms: -282.938266235 + 283.75 = 0.811733765 x = 0.811733765 Simplifying x = 0.811733765Solution
The solution to the problem is based on the solutions from the subproblems. x = {566.688266235, 0.811733765}
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