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Simplifying 8x2 + -1x + -1 = 0 Reorder the terms: -1 + -1x + 8x2 = 0 Solving -1 + -1x + 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 -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 = 0.125 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 0.125 + 0.00390625 Combine like terms: 0.125 + 0.00390625 = 0.12890625 0.00390625 + -0.125x + x2 = 0.12890625 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 0.12890625 Calculate the square root of the right side: 0.359035165 Break this problem into two subproblems by setting (x + -0.0625) equal to 0.359035165 and -0.359035165.Subproblem 1
x + -0.0625 = 0.359035165 Simplifying x + -0.0625 = 0.359035165 Reorder the terms: -0.0625 + x = 0.359035165 Solving -0.0625 + x = 0.359035165 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 = 0.359035165 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 0.359035165 + 0.0625 x = 0.359035165 + 0.0625 Combine like terms: 0.359035165 + 0.0625 = 0.421535165 x = 0.421535165 Simplifying x = 0.421535165Subproblem 2
x + -0.0625 = -0.359035165 Simplifying x + -0.0625 = -0.359035165 Reorder the terms: -0.0625 + x = -0.359035165 Solving -0.0625 + x = -0.359035165 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 = -0.359035165 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -0.359035165 + 0.0625 x = -0.359035165 + 0.0625 Combine like terms: -0.359035165 + 0.0625 = -0.296535165 x = -0.296535165 Simplifying x = -0.296535165Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.421535165, -0.296535165}
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