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Simplifying 0.51x2 + 80x + -1880 = 0 Reorder the terms: -1880 + 80x + 0.51x2 = 0 Solving -1880 + 80x + 0.51x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.51 the coefficient of the squared term: Divide each side by '0.51'. -3686.27451 + 156.8627451x + x2 = 0 Move the constant term to the right: Add '3686.27451' to each side of the equation. -3686.27451 + 156.8627451x + 3686.27451 + x2 = 0 + 3686.27451 Reorder the terms: -3686.27451 + 3686.27451 + 156.8627451x + x2 = 0 + 3686.27451 Combine like terms: -3686.27451 + 3686.27451 = 0.00000 0.00000 + 156.8627451x + x2 = 0 + 3686.27451 156.8627451x + x2 = 0 + 3686.27451 Combine like terms: 0 + 3686.27451 = 3686.27451 156.8627451x + x2 = 3686.27451 The x term is 156.8627451x. Take half its coefficient (78.43137255). Square it (6151.480200) and add it to both sides. Add '6151.480200' to each side of the equation. 156.8627451x + 6151.480200 + x2 = 3686.27451 + 6151.480200 Reorder the terms: 6151.480200 + 156.8627451x + x2 = 3686.27451 + 6151.480200 Combine like terms: 3686.27451 + 6151.480200 = 9837.75471 6151.480200 + 156.8627451x + x2 = 9837.75471 Factor a perfect square on the left side: (x + 78.43137255)(x + 78.43137255) = 9837.75471 Calculate the square root of the right side: 99.185456142 Break this problem into two subproblems by setting (x + 78.43137255) equal to 99.185456142 and -99.185456142.Subproblem 1
x + 78.43137255 = 99.185456142 Simplifying x + 78.43137255 = 99.185456142 Reorder the terms: 78.43137255 + x = 99.185456142 Solving 78.43137255 + x = 99.185456142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-78.43137255' to each side of the equation. 78.43137255 + -78.43137255 + x = 99.185456142 + -78.43137255 Combine like terms: 78.43137255 + -78.43137255 = 0.00000000 0.00000000 + x = 99.185456142 + -78.43137255 x = 99.185456142 + -78.43137255 Combine like terms: 99.185456142 + -78.43137255 = 20.754083592 x = 20.754083592 Simplifying x = 20.754083592Subproblem 2
x + 78.43137255 = -99.185456142 Simplifying x + 78.43137255 = -99.185456142 Reorder the terms: 78.43137255 + x = -99.185456142 Solving 78.43137255 + x = -99.185456142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-78.43137255' to each side of the equation. 78.43137255 + -78.43137255 + x = -99.185456142 + -78.43137255 Combine like terms: 78.43137255 + -78.43137255 = 0.00000000 0.00000000 + x = -99.185456142 + -78.43137255 x = -99.185456142 + -78.43137255 Combine like terms: -99.185456142 + -78.43137255 = -177.616828692 x = -177.616828692 Simplifying x = -177.616828692Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.754083592, -177.616828692}
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