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Simplifying 0 = 13250x + -1(124705 + -4x2 + 2880x) Reorder the terms: 0 = 13250x + -1(124705 + 2880x + -4x2) 0 = 13250x + (124705 * -1 + 2880x * -1 + -4x2 * -1) 0 = 13250x + (-124705 + -2880x + 4x2) Reorder the terms: 0 = -124705 + 13250x + -2880x + 4x2 Combine like terms: 13250x + -2880x = 10370x 0 = -124705 + 10370x + 4x2 Solving 0 = -124705 + 10370x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 124705 = 124705 124705 + -10370x + -4x2 = -124705 + 10370x + 4x2 + 124705 + -10370x + -4x2 Reorder the terms: 124705 + -10370x + -4x2 = -124705 + 124705 + 10370x + -10370x + 4x2 + -4x2 Combine like terms: -124705 + 124705 = 0 124705 + -10370x + -4x2 = 0 + 10370x + -10370x + 4x2 + -4x2 124705 + -10370x + -4x2 = 10370x + -10370x + 4x2 + -4x2 Combine like terms: 10370x + -10370x = 0 124705 + -10370x + -4x2 = 0 + 4x2 + -4x2 124705 + -10370x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 124705 + -10370x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -31176.25 + 2592.5x + x2 = 0 Move the constant term to the right: Add '31176.25' to each side of the equation. -31176.25 + 2592.5x + 31176.25 + x2 = 0 + 31176.25 Reorder the terms: -31176.25 + 31176.25 + 2592.5x + x2 = 0 + 31176.25 Combine like terms: -31176.25 + 31176.25 = 0.00 0.00 + 2592.5x + x2 = 0 + 31176.25 2592.5x + x2 = 0 + 31176.25 Combine like terms: 0 + 31176.25 = 31176.25 2592.5x + x2 = 31176.25 The x term is 2592.5x. Take half its coefficient (1296.25). Square it (1680264.063) and add it to both sides. Add '1680264.063' to each side of the equation. 2592.5x + 1680264.063 + x2 = 31176.25 + 1680264.063 Reorder the terms: 1680264.063 + 2592.5x + x2 = 31176.25 + 1680264.063 Combine like terms: 31176.25 + 1680264.063 = 1711440.313 1680264.063 + 2592.5x + x2 = 1711440.313 Factor a perfect square on the left side: (x + 1296.25)(x + 1296.25) = 1711440.313 Calculate the square root of the right side: 1308.220284585 Break this problem into two subproblems by setting (x + 1296.25) equal to 1308.220284585 and -1308.220284585.Subproblem 1
x + 1296.25 = 1308.220284585 Simplifying x + 1296.25 = 1308.220284585 Reorder the terms: 1296.25 + x = 1308.220284585 Solving 1296.25 + x = 1308.220284585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1296.25' to each side of the equation. 1296.25 + -1296.25 + x = 1308.220284585 + -1296.25 Combine like terms: 1296.25 + -1296.25 = 0.00 0.00 + x = 1308.220284585 + -1296.25 x = 1308.220284585 + -1296.25 Combine like terms: 1308.220284585 + -1296.25 = 11.970284585 x = 11.970284585 Simplifying x = 11.970284585Subproblem 2
x + 1296.25 = -1308.220284585 Simplifying x + 1296.25 = -1308.220284585 Reorder the terms: 1296.25 + x = -1308.220284585 Solving 1296.25 + x = -1308.220284585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1296.25' to each side of the equation. 1296.25 + -1296.25 + x = -1308.220284585 + -1296.25 Combine like terms: 1296.25 + -1296.25 = 0.00 0.00 + x = -1308.220284585 + -1296.25 x = -1308.220284585 + -1296.25 Combine like terms: -1308.220284585 + -1296.25 = -2604.470284585 x = -2604.470284585 Simplifying x = -2604.470284585Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.970284585, -2604.470284585}
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