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Simplifying -8x2 + x + -1 = 0 Reorder the terms: -1 + x + -8x2 = 0 Solving -1 + x + -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'. 0.125 + -0.125x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -0.125x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -0.125x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -0.125x + x2 = 0 + -0.125 -0.125x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -0.125x + x2 = -0.125 The x term is x. 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. -0.125x + 0.25 + x2 = -0.125 + 0.25 Reorder the terms: 0.25 + -0.125x + x2 = -0.125 + 0.25 Combine like terms: -0.125 + 0.25 = 0.125 0.25 + -0.125x + x2 = 0.125 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.125 Calculate the square root of the right side: 0.353553391 Break this problem into two subproblems by setting (x + 0.5) equal to 0.353553391 and -0.353553391.Subproblem 1
x + 0.5 = 0.353553391 Simplifying x + 0.5 = 0.353553391 Reorder the terms: 0.5 + x = 0.353553391 Solving 0.5 + x = 0.353553391 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 = 0.353553391 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.353553391 + -0.5 x = 0.353553391 + -0.5 Combine like terms: 0.353553391 + -0.5 = -0.146446609 x = -0.146446609 Simplifying x = -0.146446609Subproblem 2
x + 0.5 = -0.353553391 Simplifying x + 0.5 = -0.353553391 Reorder the terms: 0.5 + x = -0.353553391 Solving 0.5 + x = -0.353553391 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 = -0.353553391 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.353553391 + -0.5 x = -0.353553391 + -0.5 Combine like terms: -0.353553391 + -0.5 = -0.853553391 x = -0.853553391 Simplifying x = -0.853553391Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.146446609, -0.853553391}
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