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Simplifying 1.76x2 + -3.25x + -5000 = 0 Reorder the terms: -5000 + -3.25x + 1.76x2 = 0 Solving -5000 + -3.25x + 1.76x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.76 the coefficient of the squared term: Divide each side by '1.76'. -2840.909091 + -1.846590909x + x2 = 0 Move the constant term to the right: Add '2840.909091' to each side of the equation. -2840.909091 + -1.846590909x + 2840.909091 + x2 = 0 + 2840.909091 Reorder the terms: -2840.909091 + 2840.909091 + -1.846590909x + x2 = 0 + 2840.909091 Combine like terms: -2840.909091 + 2840.909091 = 0.000000 0.000000 + -1.846590909x + x2 = 0 + 2840.909091 -1.846590909x + x2 = 0 + 2840.909091 Combine like terms: 0 + 2840.909091 = 2840.909091 -1.846590909x + x2 = 2840.909091 The x term is -1.846590909x. Take half its coefficient (-0.9232954545). Square it (0.8524744963) and add it to both sides. Add '0.8524744963' to each side of the equation. -1.846590909x + 0.8524744963 + x2 = 2840.909091 + 0.8524744963 Reorder the terms: 0.8524744963 + -1.846590909x + x2 = 2840.909091 + 0.8524744963 Combine like terms: 2840.909091 + 0.8524744963 = 2841.7615654963 0.8524744963 + -1.846590909x + x2 = 2841.7615654963 Factor a perfect square on the left side: (x + -0.9232954545)(x + -0.9232954545) = 2841.7615654963 Calculate the square root of the right side: 53.30817541 Break this problem into two subproblems by setting (x + -0.9232954545) equal to 53.30817541 and -53.30817541.Subproblem 1
x + -0.9232954545 = 53.30817541 Simplifying x + -0.9232954545 = 53.30817541 Reorder the terms: -0.9232954545 + x = 53.30817541 Solving -0.9232954545 + x = 53.30817541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9232954545' to each side of the equation. -0.9232954545 + 0.9232954545 + x = 53.30817541 + 0.9232954545 Combine like terms: -0.9232954545 + 0.9232954545 = 0.0000000000 0.0000000000 + x = 53.30817541 + 0.9232954545 x = 53.30817541 + 0.9232954545 Combine like terms: 53.30817541 + 0.9232954545 = 54.2314708645 x = 54.2314708645 Simplifying x = 54.2314708645Subproblem 2
x + -0.9232954545 = -53.30817541 Simplifying x + -0.9232954545 = -53.30817541 Reorder the terms: -0.9232954545 + x = -53.30817541 Solving -0.9232954545 + x = -53.30817541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9232954545' to each side of the equation. -0.9232954545 + 0.9232954545 + x = -53.30817541 + 0.9232954545 Combine like terms: -0.9232954545 + 0.9232954545 = 0.0000000000 0.0000000000 + x = -53.30817541 + 0.9232954545 x = -53.30817541 + 0.9232954545 Combine like terms: -53.30817541 + 0.9232954545 = -52.3848799555 x = -52.3848799555 Simplifying x = -52.3848799555Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.2314708645, -52.3848799555}
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