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Simplifying x2 + -1x + -1 + 1 = 15 + -7x2 Reorder the terms: -1 + 1 + -1x + x2 = 15 + -7x2 Combine like terms: -1 + 1 = 0 0 + -1x + x2 = 15 + -7x2 -1x + x2 = 15 + -7x2 Solving -1x + x2 = 15 + -7x2 Solving for variable 'x'. Reorder the terms: -15 + -1x + x2 + 7x2 = 15 + -7x2 + -15 + 7x2 Combine like terms: x2 + 7x2 = 8x2 -15 + -1x + 8x2 = 15 + -7x2 + -15 + 7x2 Reorder the terms: -15 + -1x + 8x2 = 15 + -15 + -7x2 + 7x2 Combine like terms: 15 + -15 = 0 -15 + -1x + 8x2 = 0 + -7x2 + 7x2 -15 + -1x + 8x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 -15 + -1x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.875 + -0.125x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -0.125x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -0.125x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -0.125x + x2 = 0 + 1.875 -0.125x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -0.125x + x2 = 1.875 The x term is -0.125x. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125x + 0.00390625 + x2 = 1.875 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 1.875 + 0.00390625 Combine like terms: 1.875 + 0.00390625 = 1.87890625 0.00390625 + -0.125x + x2 = 1.87890625 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 1.87890625 Calculate the square root of the right side: 1.370732012 Break this problem into two subproblems by setting (x + -0.0625) equal to 1.370732012 and -1.370732012.Subproblem 1
x + -0.0625 = 1.370732012 Simplifying x + -0.0625 = 1.370732012 Reorder the terms: -0.0625 + x = 1.370732012 Solving -0.0625 + x = 1.370732012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = 1.370732012 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 1.370732012 + 0.0625 x = 1.370732012 + 0.0625 Combine like terms: 1.370732012 + 0.0625 = 1.433232012 x = 1.433232012 Simplifying x = 1.433232012Subproblem 2
x + -0.0625 = -1.370732012 Simplifying x + -0.0625 = -1.370732012 Reorder the terms: -0.0625 + x = -1.370732012 Solving -0.0625 + x = -1.370732012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = -1.370732012 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -1.370732012 + 0.0625 x = -1.370732012 + 0.0625 Combine like terms: -1.370732012 + 0.0625 = -1.308232012 x = -1.308232012 Simplifying x = -1.308232012Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.433232012, -1.308232012}
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