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Simplifying 125x2 + -1822x + -4008 = 0 Reorder the terms: -4008 + -1822x + 125x2 = 0 Solving -4008 + -1822x + 125x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 125 the coefficient of the squared term: Divide each side by '125'. -32.064 + -14.576x + x2 = 0 Move the constant term to the right: Add '32.064' to each side of the equation. -32.064 + -14.576x + 32.064 + x2 = 0 + 32.064 Reorder the terms: -32.064 + 32.064 + -14.576x + x2 = 0 + 32.064 Combine like terms: -32.064 + 32.064 = 0.000 0.000 + -14.576x + x2 = 0 + 32.064 -14.576x + x2 = 0 + 32.064 Combine like terms: 0 + 32.064 = 32.064 -14.576x + x2 = 32.064 The x term is -14.576x. Take half its coefficient (-7.288). Square it (53.114944) and add it to both sides. Add '53.114944' to each side of the equation. -14.576x + 53.114944 + x2 = 32.064 + 53.114944 Reorder the terms: 53.114944 + -14.576x + x2 = 32.064 + 53.114944 Combine like terms: 32.064 + 53.114944 = 85.178944 53.114944 + -14.576x + x2 = 85.178944 Factor a perfect square on the left side: (x + -7.288)(x + -7.288) = 85.178944 Calculate the square root of the right side: 9.229243956 Break this problem into two subproblems by setting (x + -7.288) equal to 9.229243956 and -9.229243956.Subproblem 1
x + -7.288 = 9.229243956 Simplifying x + -7.288 = 9.229243956 Reorder the terms: -7.288 + x = 9.229243956 Solving -7.288 + x = 9.229243956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.288' to each side of the equation. -7.288 + 7.288 + x = 9.229243956 + 7.288 Combine like terms: -7.288 + 7.288 = 0.000 0.000 + x = 9.229243956 + 7.288 x = 9.229243956 + 7.288 Combine like terms: 9.229243956 + 7.288 = 16.517243956 x = 16.517243956 Simplifying x = 16.517243956Subproblem 2
x + -7.288 = -9.229243956 Simplifying x + -7.288 = -9.229243956 Reorder the terms: -7.288 + x = -9.229243956 Solving -7.288 + x = -9.229243956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.288' to each side of the equation. -7.288 + 7.288 + x = -9.229243956 + 7.288 Combine like terms: -7.288 + 7.288 = 0.000 0.000 + x = -9.229243956 + 7.288 x = -9.229243956 + 7.288 Combine like terms: -9.229243956 + 7.288 = -1.941243956 x = -1.941243956 Simplifying x = -1.941243956Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.517243956, -1.941243956}
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