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Simplifying 13x2 + -634x + -2088 = 0 Reorder the terms: -2088 + -634x + 13x2 = 0 Solving -2088 + -634x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -160.6153846 + -48.76923077x + x2 = 0 Move the constant term to the right: Add '160.6153846' to each side of the equation. -160.6153846 + -48.76923077x + 160.6153846 + x2 = 0 + 160.6153846 Reorder the terms: -160.6153846 + 160.6153846 + -48.76923077x + x2 = 0 + 160.6153846 Combine like terms: -160.6153846 + 160.6153846 = 0.0000000 0.0000000 + -48.76923077x + x2 = 0 + 160.6153846 -48.76923077x + x2 = 0 + 160.6153846 Combine like terms: 0 + 160.6153846 = 160.6153846 -48.76923077x + x2 = 160.6153846 The x term is -48.76923077x. Take half its coefficient (-24.38461539). Square it (594.6094677) and add it to both sides. Add '594.6094677' to each side of the equation. -48.76923077x + 594.6094677 + x2 = 160.6153846 + 594.6094677 Reorder the terms: 594.6094677 + -48.76923077x + x2 = 160.6153846 + 594.6094677 Combine like terms: 160.6153846 + 594.6094677 = 755.2248523 594.6094677 + -48.76923077x + x2 = 755.2248523 Factor a perfect square on the left side: (x + -24.38461539)(x + -24.38461539) = 755.2248523 Calculate the square root of the right side: 27.48135463 Break this problem into two subproblems by setting (x + -24.38461539) equal to 27.48135463 and -27.48135463.Subproblem 1
x + -24.38461539 = 27.48135463 Simplifying x + -24.38461539 = 27.48135463 Reorder the terms: -24.38461539 + x = 27.48135463 Solving -24.38461539 + x = 27.48135463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.38461539' to each side of the equation. -24.38461539 + 24.38461539 + x = 27.48135463 + 24.38461539 Combine like terms: -24.38461539 + 24.38461539 = 0.00000000 0.00000000 + x = 27.48135463 + 24.38461539 x = 27.48135463 + 24.38461539 Combine like terms: 27.48135463 + 24.38461539 = 51.86597002 x = 51.86597002 Simplifying x = 51.86597002Subproblem 2
x + -24.38461539 = -27.48135463 Simplifying x + -24.38461539 = -27.48135463 Reorder the terms: -24.38461539 + x = -27.48135463 Solving -24.38461539 + x = -27.48135463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.38461539' to each side of the equation. -24.38461539 + 24.38461539 + x = -27.48135463 + 24.38461539 Combine like terms: -24.38461539 + 24.38461539 = 0.00000000 0.00000000 + x = -27.48135463 + 24.38461539 x = -27.48135463 + 24.38461539 Combine like terms: -27.48135463 + 24.38461539 = -3.09673924 x = -3.09673924 Simplifying x = -3.09673924Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.86597002, -3.09673924}
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