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Simplifying 64x2 + -16x + 1 = x Reorder the terms: 1 + -16x + 64x2 = x Solving 1 + -16x + 64x2 = x Solving for variable 'x'. Reorder the terms: 1 + -16x + -1x + 64x2 = x + -1x Combine like terms: -16x + -1x = -17x 1 + -17x + 64x2 = x + -1x Combine like terms: x + -1x = 0 1 + -17x + 64x2 = 0 Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. 0.015625 + -0.265625x + x2 = 0 Move the constant term to the right: Add '-0.015625' to each side of the equation. 0.015625 + -0.265625x + -0.015625 + x2 = 0 + -0.015625 Reorder the terms: 0.015625 + -0.015625 + -0.265625x + x2 = 0 + -0.015625 Combine like terms: 0.015625 + -0.015625 = 0.000000 0.000000 + -0.265625x + x2 = 0 + -0.015625 -0.265625x + x2 = 0 + -0.015625 Combine like terms: 0 + -0.015625 = -0.015625 -0.265625x + x2 = -0.015625 The x term is -0.265625x. Take half its coefficient (-0.1328125). Square it (0.01763916016) and add it to both sides. Add '0.01763916016' to each side of the equation. -0.265625x + 0.01763916016 + x2 = -0.015625 + 0.01763916016 Reorder the terms: 0.01763916016 + -0.265625x + x2 = -0.015625 + 0.01763916016 Combine like terms: -0.015625 + 0.01763916016 = 0.00201416016 0.01763916016 + -0.265625x + x2 = 0.00201416016 Factor a perfect square on the left side: (x + -0.1328125)(x + -0.1328125) = 0.00201416016 Calculate the square root of the right side: 0.044879396 Break this problem into two subproblems by setting (x + -0.1328125) equal to 0.044879396 and -0.044879396.Subproblem 1
x + -0.1328125 = 0.044879396 Simplifying x + -0.1328125 = 0.044879396 Reorder the terms: -0.1328125 + x = 0.044879396 Solving -0.1328125 + x = 0.044879396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1328125' to each side of the equation. -0.1328125 + 0.1328125 + x = 0.044879396 + 0.1328125 Combine like terms: -0.1328125 + 0.1328125 = 0.0000000 0.0000000 + x = 0.044879396 + 0.1328125 x = 0.044879396 + 0.1328125 Combine like terms: 0.044879396 + 0.1328125 = 0.177691896 x = 0.177691896 Simplifying x = 0.177691896Subproblem 2
x + -0.1328125 = -0.044879396 Simplifying x + -0.1328125 = -0.044879396 Reorder the terms: -0.1328125 + x = -0.044879396 Solving -0.1328125 + x = -0.044879396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1328125' to each side of the equation. -0.1328125 + 0.1328125 + x = -0.044879396 + 0.1328125 Combine like terms: -0.1328125 + 0.1328125 = 0.0000000 0.0000000 + x = -0.044879396 + 0.1328125 x = -0.044879396 + 0.1328125 Combine like terms: -0.044879396 + 0.1328125 = 0.087933104 x = 0.087933104 Simplifying x = 0.087933104Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.177691896, 0.087933104}
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