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Simplifying 2x + -1 = -8x * 8x Reorder the terms: -1 + 2x = -8x * 8x Reorder the terms for easier multiplication: -1 + 2x = -8 * 8x * x Multiply -8 * 8 -1 + 2x = -64x * x Multiply x * x -1 + 2x = -64x2 Solving -1 + 2x = -64x2 Solving for variable 'x'. Combine like terms: -64x2 + 64x2 = 0 -1 + 2x + 64x2 = 0 Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.015625 + 0.03125x + x2 = 0 Move the constant term to the right: Add '0.015625' to each side of the equation. -0.015625 + 0.03125x + 0.015625 + x2 = 0 + 0.015625 Reorder the terms: -0.015625 + 0.015625 + 0.03125x + x2 = 0 + 0.015625 Combine like terms: -0.015625 + 0.015625 = 0.000000 0.000000 + 0.03125x + x2 = 0 + 0.015625 0.03125x + x2 = 0 + 0.015625 Combine like terms: 0 + 0.015625 = 0.015625 0.03125x + x2 = 0.015625 The x term is 0.03125x. Take half its coefficient (0.015625). Square it (0.000244140625) and add it to both sides. Add '0.000244140625' to each side of the equation. 0.03125x + 0.000244140625 + x2 = 0.015625 + 0.000244140625 Reorder the terms: 0.000244140625 + 0.03125x + x2 = 0.015625 + 0.000244140625 Combine like terms: 0.015625 + 0.000244140625 = 0.015869140625 0.000244140625 + 0.03125x + x2 = 0.015869140625 Factor a perfect square on the left side: (x + 0.015625)(x + 0.015625) = 0.015869140625 Calculate the square root of the right side: 0.125972777 Break this problem into two subproblems by setting (x + 0.015625) equal to 0.125972777 and -0.125972777.Subproblem 1
x + 0.015625 = 0.125972777 Simplifying x + 0.015625 = 0.125972777 Reorder the terms: 0.015625 + x = 0.125972777 Solving 0.015625 + x = 0.125972777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.015625' to each side of the equation. 0.015625 + -0.015625 + x = 0.125972777 + -0.015625 Combine like terms: 0.015625 + -0.015625 = 0.000000 0.000000 + x = 0.125972777 + -0.015625 x = 0.125972777 + -0.015625 Combine like terms: 0.125972777 + -0.015625 = 0.110347777 x = 0.110347777 Simplifying x = 0.110347777Subproblem 2
x + 0.015625 = -0.125972777 Simplifying x + 0.015625 = -0.125972777 Reorder the terms: 0.015625 + x = -0.125972777 Solving 0.015625 + x = -0.125972777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.015625' to each side of the equation. 0.015625 + -0.015625 + x = -0.125972777 + -0.015625 Combine like terms: 0.015625 + -0.015625 = 0.000000 0.000000 + x = -0.125972777 + -0.015625 x = -0.125972777 + -0.015625 Combine like terms: -0.125972777 + -0.015625 = -0.141597777 x = -0.141597777 Simplifying x = -0.141597777Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.110347777, -0.141597777}
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