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Simplifying 0.36x2 + -7x + -7000 = 0 Reorder the terms: -7000 + -7x + 0.36x2 = 0 Solving -7000 + -7x + 0.36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.36 the coefficient of the squared term: Divide each side by '0.36'. -19444.44444 + -19.44444444x + x2 = 0 Move the constant term to the right: Add '19444.44444' to each side of the equation. -19444.44444 + -19.44444444x + 19444.44444 + x2 = 0 + 19444.44444 Reorder the terms: -19444.44444 + 19444.44444 + -19.44444444x + x2 = 0 + 19444.44444 Combine like terms: -19444.44444 + 19444.44444 = 0.00000 0.00000 + -19.44444444x + x2 = 0 + 19444.44444 -19.44444444x + x2 = 0 + 19444.44444 Combine like terms: 0 + 19444.44444 = 19444.44444 -19.44444444x + x2 = 19444.44444 The x term is -19.44444444x. Take half its coefficient (-9.72222222). Square it (94.52160490) and add it to both sides. Add '94.52160490' to each side of the equation. -19.44444444x + 94.52160490 + x2 = 19444.44444 + 94.52160490 Reorder the terms: 94.52160490 + -19.44444444x + x2 = 19444.44444 + 94.52160490 Combine like terms: 19444.44444 + 94.52160490 = 19538.9660449 94.52160490 + -19.44444444x + x2 = 19538.9660449 Factor a perfect square on the left side: (x + -9.72222222)(x + -9.72222222) = 19538.9660449 Calculate the square root of the right side: 139.781851629 Break this problem into two subproblems by setting (x + -9.72222222) equal to 139.781851629 and -139.781851629.Subproblem 1
x + -9.72222222 = 139.781851629 Simplifying x + -9.72222222 = 139.781851629 Reorder the terms: -9.72222222 + x = 139.781851629 Solving -9.72222222 + x = 139.781851629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.72222222' to each side of the equation. -9.72222222 + 9.72222222 + x = 139.781851629 + 9.72222222 Combine like terms: -9.72222222 + 9.72222222 = 0.00000000 0.00000000 + x = 139.781851629 + 9.72222222 x = 139.781851629 + 9.72222222 Combine like terms: 139.781851629 + 9.72222222 = 149.504073849 x = 149.504073849 Simplifying x = 149.504073849Subproblem 2
x + -9.72222222 = -139.781851629 Simplifying x + -9.72222222 = -139.781851629 Reorder the terms: -9.72222222 + x = -139.781851629 Solving -9.72222222 + x = -139.781851629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.72222222' to each side of the equation. -9.72222222 + 9.72222222 + x = -139.781851629 + 9.72222222 Combine like terms: -9.72222222 + 9.72222222 = 0.00000000 0.00000000 + x = -139.781851629 + 9.72222222 x = -139.781851629 + 9.72222222 Combine like terms: -139.781851629 + 9.72222222 = -130.059629409 x = -130.059629409 Simplifying x = -130.059629409Solution
The solution to the problem is based on the solutions from the subproblems. x = {149.504073849, -130.059629409}
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