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Simplifying 8x2 + -115x + -115 = 0 Reorder the terms: -115 + -115x + 8x2 = 0 Solving -115 + -115x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -14.375 + -14.375x + x2 = 0 Move the constant term to the right: Add '14.375' to each side of the equation. -14.375 + -14.375x + 14.375 + x2 = 0 + 14.375 Reorder the terms: -14.375 + 14.375 + -14.375x + x2 = 0 + 14.375 Combine like terms: -14.375 + 14.375 = 0.000 0.000 + -14.375x + x2 = 0 + 14.375 -14.375x + x2 = 0 + 14.375 Combine like terms: 0 + 14.375 = 14.375 -14.375x + x2 = 14.375 The x term is -14.375x. Take half its coefficient (-7.1875). Square it (51.66015625) and add it to both sides. Add '51.66015625' to each side of the equation. -14.375x + 51.66015625 + x2 = 14.375 + 51.66015625 Reorder the terms: 51.66015625 + -14.375x + x2 = 14.375 + 51.66015625 Combine like terms: 14.375 + 51.66015625 = 66.03515625 51.66015625 + -14.375x + x2 = 66.03515625 Factor a perfect square on the left side: (x + -7.1875)(x + -7.1875) = 66.03515625 Calculate the square root of the right side: 8.126201834 Break this problem into two subproblems by setting (x + -7.1875) equal to 8.126201834 and -8.126201834.Subproblem 1
x + -7.1875 = 8.126201834 Simplifying x + -7.1875 = 8.126201834 Reorder the terms: -7.1875 + x = 8.126201834 Solving -7.1875 + x = 8.126201834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.1875' to each side of the equation. -7.1875 + 7.1875 + x = 8.126201834 + 7.1875 Combine like terms: -7.1875 + 7.1875 = 0.0000 0.0000 + x = 8.126201834 + 7.1875 x = 8.126201834 + 7.1875 Combine like terms: 8.126201834 + 7.1875 = 15.313701834 x = 15.313701834 Simplifying x = 15.313701834Subproblem 2
x + -7.1875 = -8.126201834 Simplifying x + -7.1875 = -8.126201834 Reorder the terms: -7.1875 + x = -8.126201834 Solving -7.1875 + x = -8.126201834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.1875' to each side of the equation. -7.1875 + 7.1875 + x = -8.126201834 + 7.1875 Combine like terms: -7.1875 + 7.1875 = 0.0000 0.0000 + x = -8.126201834 + 7.1875 x = -8.126201834 + 7.1875 Combine like terms: -8.126201834 + 7.1875 = -0.938701834 x = -0.938701834 Simplifying x = -0.938701834Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.313701834, -0.938701834}
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