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Simplifying 0 = -8x2 + -14x + 107 Reorder the terms: 0 = 107 + -14x + -8x2 Solving 0 = 107 + -14x + -8x2 Solving for variable 'x'. Combine like terms: 0 + -107 = -107 -107 + 14x + 8x2 = 107 + -14x + -8x2 + -107 + 14x + 8x2 Reorder the terms: -107 + 14x + 8x2 = 107 + -107 + -14x + 14x + -8x2 + 8x2 Combine like terms: 107 + -107 = 0 -107 + 14x + 8x2 = 0 + -14x + 14x + -8x2 + 8x2 -107 + 14x + 8x2 = -14x + 14x + -8x2 + 8x2 Combine like terms: -14x + 14x = 0 -107 + 14x + 8x2 = 0 + -8x2 + 8x2 -107 + 14x + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 -107 + 14x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -13.375 + 1.75x + x2 = 0 Move the constant term to the right: Add '13.375' to each side of the equation. -13.375 + 1.75x + 13.375 + x2 = 0 + 13.375 Reorder the terms: -13.375 + 13.375 + 1.75x + x2 = 0 + 13.375 Combine like terms: -13.375 + 13.375 = 0.000 0.000 + 1.75x + x2 = 0 + 13.375 1.75x + x2 = 0 + 13.375 Combine like terms: 0 + 13.375 = 13.375 1.75x + x2 = 13.375 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 13.375 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 13.375 + 0.765625 Combine like terms: 13.375 + 0.765625 = 14.140625 0.765625 + 1.75x + x2 = 14.140625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 14.140625 Calculate the square root of the right side: 3.760402239 Break this problem into two subproblems by setting (x + 0.875) equal to 3.760402239 and -3.760402239.Subproblem 1
x + 0.875 = 3.760402239 Simplifying x + 0.875 = 3.760402239 Reorder the terms: 0.875 + x = 3.760402239 Solving 0.875 + x = 3.760402239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 3.760402239 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 3.760402239 + -0.875 x = 3.760402239 + -0.875 Combine like terms: 3.760402239 + -0.875 = 2.885402239 x = 2.885402239 Simplifying x = 2.885402239Subproblem 2
x + 0.875 = -3.760402239 Simplifying x + 0.875 = -3.760402239 Reorder the terms: 0.875 + x = -3.760402239 Solving 0.875 + x = -3.760402239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -3.760402239 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -3.760402239 + -0.875 x = -3.760402239 + -0.875 Combine like terms: -3.760402239 + -0.875 = -4.635402239 x = -4.635402239 Simplifying x = -4.635402239Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.885402239, -4.635402239}
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