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Simplifying (8x + -1)(8x + -1) = 2 Reorder the terms: (-1 + 8x)(8x + -1) = 2 Reorder the terms: (-1 + 8x)(-1 + 8x) = 2 Multiply (-1 + 8x) * (-1 + 8x) (-1(-1 + 8x) + 8x * (-1 + 8x)) = 2 ((-1 * -1 + 8x * -1) + 8x * (-1 + 8x)) = 2 ((1 + -8x) + 8x * (-1 + 8x)) = 2 (1 + -8x + (-1 * 8x + 8x * 8x)) = 2 (1 + -8x + (-8x + 64x2)) = 2 Combine like terms: -8x + -8x = -16x (1 + -16x + 64x2) = 2 Solving 1 + -16x + 64x2 = 2 Solving for variable 'x'. Reorder the terms: 1 + -2 + -16x + 64x2 = 2 + -2 Combine like terms: 1 + -2 = -1 -1 + -16x + 64x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -1 + -16x + 64x2 = 0 Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.015625 + -0.25x + x2 = 0 Move the constant term to the right: Add '0.015625' to each side of the equation. -0.015625 + -0.25x + 0.015625 + x2 = 0 + 0.015625 Reorder the terms: -0.015625 + 0.015625 + -0.25x + x2 = 0 + 0.015625 Combine like terms: -0.015625 + 0.015625 = 0.000000 0.000000 + -0.25x + x2 = 0 + 0.015625 -0.25x + x2 = 0 + 0.015625 Combine like terms: 0 + 0.015625 = 0.015625 -0.25x + x2 = 0.015625 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 0.015625 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.015625 + 0.015625 Combine like terms: 0.015625 + 0.015625 = 0.03125 0.015625 + -0.25x + x2 = 0.03125 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.03125 Calculate the square root of the right side: 0.176776695 Break this problem into two subproblems by setting (x + -0.125) equal to 0.176776695 and -0.176776695.Subproblem 1
x + -0.125 = 0.176776695 Simplifying x + -0.125 = 0.176776695 Reorder the terms: -0.125 + x = 0.176776695 Solving -0.125 + x = 0.176776695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.176776695 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.176776695 + 0.125 x = 0.176776695 + 0.125 Combine like terms: 0.176776695 + 0.125 = 0.301776695 x = 0.301776695 Simplifying x = 0.301776695Subproblem 2
x + -0.125 = -0.176776695 Simplifying x + -0.125 = -0.176776695 Reorder the terms: -0.125 + x = -0.176776695 Solving -0.125 + x = -0.176776695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.176776695 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.176776695 + 0.125 x = -0.176776695 + 0.125 Combine like terms: -0.176776695 + 0.125 = -0.051776695 x = -0.051776695 Simplifying x = -0.051776695Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.301776695, -0.051776695}
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