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Simplifying 0 = 125000 + (-4x2 + 2880x + -295) Reorder the terms: 0 = 125000 + (-295 + 2880x + -4x2) Remove parenthesis around (-295 + 2880x + -4x2) 0 = 125000 + -295 + 2880x + -4x2 Combine like terms: 125000 + -295 = 124705 0 = 124705 + 2880x + -4x2 Solving 0 = 124705 + 2880x + -4x2 Solving for variable 'x'. Combine like terms: 0 + -124705 = -124705 -124705 + -2880x + 4x2 = 124705 + 2880x + -4x2 + -124705 + -2880x + 4x2 Reorder the terms: -124705 + -2880x + 4x2 = 124705 + -124705 + 2880x + -2880x + -4x2 + 4x2 Combine like terms: 124705 + -124705 = 0 -124705 + -2880x + 4x2 = 0 + 2880x + -2880x + -4x2 + 4x2 -124705 + -2880x + 4x2 = 2880x + -2880x + -4x2 + 4x2 Combine like terms: 2880x + -2880x = 0 -124705 + -2880x + 4x2 = 0 + -4x2 + 4x2 -124705 + -2880x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -124705 + -2880x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -31176.25 + -720x + x2 = 0 Move the constant term to the right: Add '31176.25' to each side of the equation. -31176.25 + -720x + 31176.25 + x2 = 0 + 31176.25 Reorder the terms: -31176.25 + 31176.25 + -720x + x2 = 0 + 31176.25 Combine like terms: -31176.25 + 31176.25 = 0.00 0.00 + -720x + x2 = 0 + 31176.25 -720x + x2 = 0 + 31176.25 Combine like terms: 0 + 31176.25 = 31176.25 -720x + x2 = 31176.25 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 = 31176.25 + 129600 Reorder the terms: 129600 + -720x + x2 = 31176.25 + 129600 Combine like terms: 31176.25 + 129600 = 160776.25 129600 + -720x + x2 = 160776.25 Factor a perfect square on the left side: (x + -360)(x + -360) = 160776.25 Calculate the square root of the right side: 400.969138463 Break this problem into two subproblems by setting (x + -360) equal to 400.969138463 and -400.969138463.Subproblem 1
x + -360 = 400.969138463 Simplifying x + -360 = 400.969138463 Reorder the terms: -360 + x = 400.969138463 Solving -360 + x = 400.969138463 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 = 400.969138463 + 360 Combine like terms: -360 + 360 = 0 0 + x = 400.969138463 + 360 x = 400.969138463 + 360 Combine like terms: 400.969138463 + 360 = 760.969138463 x = 760.969138463 Simplifying x = 760.969138463Subproblem 2
x + -360 = -400.969138463 Simplifying x + -360 = -400.969138463 Reorder the terms: -360 + x = -400.969138463 Solving -360 + x = -400.969138463 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 = -400.969138463 + 360 Combine like terms: -360 + 360 = 0 0 + x = -400.969138463 + 360 x = -400.969138463 + 360 Combine like terms: -400.969138463 + 360 = -40.969138463 x = -40.969138463 Simplifying x = -40.969138463Solution
The solution to the problem is based on the solutions from the subproblems. x = {760.969138463, -40.969138463}
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