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Simplifying -1x2 + 720x + -2500 = 0 Reorder the terms: -2500 + 720x + -1x2 = 0 Solving -2500 + 720x + -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'. 2500 + -720x + x2 = 0 Move the constant term to the right: Add '-2500' to each side of the equation. 2500 + -720x + -2500 + x2 = 0 + -2500 Reorder the terms: 2500 + -2500 + -720x + x2 = 0 + -2500 Combine like terms: 2500 + -2500 = 0 0 + -720x + x2 = 0 + -2500 -720x + x2 = 0 + -2500 Combine like terms: 0 + -2500 = -2500 -720x + x2 = -2500 The x term is -720x. Take half its coefficient (-360). Square it (129600) and add it to both sides. Add '129600' to each side of the equation. -720x + 129600 + x2 = -2500 + 129600 Reorder the terms: 129600 + -720x + x2 = -2500 + 129600 Combine like terms: -2500 + 129600 = 127100 129600 + -720x + x2 = 127100 Factor a perfect square on the left side: (x + -360)(x + -360) = 127100 Calculate the square root of the right side: 356.5108694 Break this problem into two subproblems by setting (x + -360) equal to 356.5108694 and -356.5108694.Subproblem 1
x + -360 = 356.5108694 Simplifying x + -360 = 356.5108694 Reorder the terms: -360 + x = 356.5108694 Solving -360 + x = 356.5108694 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '360' to each side of the equation. -360 + 360 + x = 356.5108694 + 360 Combine like terms: -360 + 360 = 0 0 + x = 356.5108694 + 360 x = 356.5108694 + 360 Combine like terms: 356.5108694 + 360 = 716.5108694 x = 716.5108694 Simplifying x = 716.5108694Subproblem 2
x + -360 = -356.5108694 Simplifying x + -360 = -356.5108694 Reorder the terms: -360 + x = -356.5108694 Solving -360 + x = -356.5108694 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '360' to each side of the equation. -360 + 360 + x = -356.5108694 + 360 Combine like terms: -360 + 360 = 0 0 + x = -356.5108694 + 360 x = -356.5108694 + 360 Combine like terms: -356.5108694 + 360 = 3.4891306 x = 3.4891306 Simplifying x = 3.4891306Solution
The solution to the problem is based on the solutions from the subproblems. x = {716.5108694, 3.4891306}
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