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Simplifying 64x2 + 8x + 0.25 = 0 Reorder the terms: 0.25 + 8x + 64x2 = 0 Solving 0.25 + 8x + 64x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. 0.00390625 + 0.125x + x2 = 0 Move the constant term to the right: Add '-0.00390625' to each side of the equation. 0.00390625 + 0.125x + -0.00390625 + x2 = 0 + -0.00390625 Reorder the terms: 0.00390625 + -0.00390625 + 0.125x + x2 = 0 + -0.00390625 Combine like terms: 0.00390625 + -0.00390625 = 0.00000000 0.00000000 + 0.125x + x2 = 0 + -0.00390625 0.125x + x2 = 0 + -0.00390625 Combine like terms: 0 + -0.00390625 = -0.00390625 0.125x + x2 = -0.00390625 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 = -0.00390625 + 0.00390625 Reorder the terms: 0.00390625 + 0.125x + x2 = -0.00390625 + 0.00390625 Combine like terms: -0.00390625 + 0.00390625 = 0.00000000 0.00390625 + 0.125x + x2 = 0.00000000 Factor a perfect square on the left side: (x + 0.0625)(x + 0.0625) = 0.00000000 Calculate the square root of the right side: 0.00000000 Break this problem into two subproblems by setting (x + 0.0625) equal to 0.00000000 and 0.00000000.Subproblem 1
x + 0.0625 = 0.00000000 Simplifying x + 0.0625 = 0.00000000 Reorder the terms: 0.0625 + x = 0.00000000 Solving 0.0625 + x = 0.00000000 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 = 0.00000000 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = 0.00000000 + -0.0625 x = 0.00000000 + -0.0625 Combine like terms: 0.00000000 + -0.0625 = -0.0625 x = -0.0625 Simplifying x = -0.0625Subproblem 2
x + 0.0625 = 0.00000000 Simplifying x + 0.0625 = 0.00000000 Reorder the terms: 0.0625 + x = 0.00000000 Solving 0.0625 + x = 0.00000000 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 = 0.00000000 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = 0.00000000 + -0.0625 x = 0.00000000 + -0.0625 Combine like terms: 0.00000000 + -0.0625 = -0.0625 x = -0.0625 Simplifying x = -0.0625Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0625, -0.0625}
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