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Simplifying -1x2 + -590x + 22000 = 0 Reorder the terms: 22000 + -590x + -1x2 = 0 Solving 22000 + -590x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -22000 + 590x + x2 = 0 Move the constant term to the right: Add '22000' to each side of the equation. -22000 + 590x + 22000 + x2 = 0 + 22000 Reorder the terms: -22000 + 22000 + 590x + x2 = 0 + 22000 Combine like terms: -22000 + 22000 = 0 0 + 590x + x2 = 0 + 22000 590x + x2 = 0 + 22000 Combine like terms: 0 + 22000 = 22000 590x + x2 = 22000 The x term is 590x. Take half its coefficient (295). Square it (87025) and add it to both sides. Add '87025' to each side of the equation. 590x + 87025 + x2 = 22000 + 87025 Reorder the terms: 87025 + 590x + x2 = 22000 + 87025 Combine like terms: 22000 + 87025 = 109025 87025 + 590x + x2 = 109025 Factor a perfect square on the left side: (x + 295)(x + 295) = 109025 Calculate the square root of the right side: 330.189339622 Break this problem into two subproblems by setting (x + 295) equal to 330.189339622 and -330.189339622.Subproblem 1
x + 295 = 330.189339622 Simplifying x + 295 = 330.189339622 Reorder the terms: 295 + x = 330.189339622 Solving 295 + x = 330.189339622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-295' to each side of the equation. 295 + -295 + x = 330.189339622 + -295 Combine like terms: 295 + -295 = 0 0 + x = 330.189339622 + -295 x = 330.189339622 + -295 Combine like terms: 330.189339622 + -295 = 35.189339622 x = 35.189339622 Simplifying x = 35.189339622Subproblem 2
x + 295 = -330.189339622 Simplifying x + 295 = -330.189339622 Reorder the terms: 295 + x = -330.189339622 Solving 295 + x = -330.189339622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-295' to each side of the equation. 295 + -295 + x = -330.189339622 + -295 Combine like terms: 295 + -295 = 0 0 + x = -330.189339622 + -295 x = -330.189339622 + -295 Combine like terms: -330.189339622 + -295 = -625.189339622 x = -625.189339622 Simplifying x = -625.189339622Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.189339622, -625.189339622}
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