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Simplifying 8x^{2}+ -8x + -1 = 0 Reorder the terms: -1 + -8x + 8x^{2}= 0 Solving -1 + -8x + 8x^{2}= 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'. -0.125 + -1x + x^{2}= 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -1x + 0.125 + x^{2}= 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -1x + x^{2}= 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -1x + x^{2}= 0 + 0.125 -1x + x^{2}= 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -1x + x^{2}= 0.125 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x^{2}= 0.125 + 0.25 Reorder the terms: 0.25 + -1x + x^{2}= 0.125 + 0.25 Combine like terms: 0.125 + 0.25 = 0.375 0.25 + -1x + x^{2}= 0.375 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.375 Calculate the square root of the right side: 0.612372436 Break this problem into two subproblems by setting (x + -0.5) equal to 0.612372436 and -0.612372436.## Subproblem 1

x + -0.5 = 0.612372436 Simplifying x + -0.5 = 0.612372436 Reorder the terms: -0.5 + x = 0.612372436 Solving -0.5 + x = 0.612372436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.612372436 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.612372436 + 0.5 x = 0.612372436 + 0.5 Combine like terms: 0.612372436 + 0.5 = 1.112372436 x = 1.112372436 Simplifying x = 1.112372436## Subproblem 2

x + -0.5 = -0.612372436 Simplifying x + -0.5 = -0.612372436 Reorder the terms: -0.5 + x = -0.612372436 Solving -0.5 + x = -0.612372436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.612372436 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.612372436 + 0.5 x = -0.612372436 + 0.5 Combine like terms: -0.612372436 + 0.5 = -0.112372436 x = -0.112372436 Simplifying x = -0.112372436## Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.112372436, -0.112372436}

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