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Simplifying 56x2 + -7x + -1 = 0 Reorder the terms: -1 + -7x + 56x2 = 0 Solving -1 + -7x + 56x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 56 the coefficient of the squared term: Divide each side by '56'. -0.01785714286 + -0.125x + x2 = 0 Move the constant term to the right: Add '0.01785714286' to each side of the equation. -0.01785714286 + -0.125x + 0.01785714286 + x2 = 0 + 0.01785714286 Reorder the terms: -0.01785714286 + 0.01785714286 + -0.125x + x2 = 0 + 0.01785714286 Combine like terms: -0.01785714286 + 0.01785714286 = 0.00000000000 0.00000000000 + -0.125x + x2 = 0 + 0.01785714286 -0.125x + x2 = 0 + 0.01785714286 Combine like terms: 0 + 0.01785714286 = 0.01785714286 -0.125x + x2 = 0.01785714286 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 = 0.01785714286 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 0.01785714286 + 0.00390625 Combine like terms: 0.01785714286 + 0.00390625 = 0.02176339286 0.00390625 + -0.125x + x2 = 0.02176339286 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 0.02176339286 Calculate the square root of the right side: 0.147524211 Break this problem into two subproblems by setting (x + -0.0625) equal to 0.147524211 and -0.147524211.Subproblem 1
x + -0.0625 = 0.147524211 Simplifying x + -0.0625 = 0.147524211 Reorder the terms: -0.0625 + x = 0.147524211 Solving -0.0625 + x = 0.147524211 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 = 0.147524211 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 0.147524211 + 0.0625 x = 0.147524211 + 0.0625 Combine like terms: 0.147524211 + 0.0625 = 0.210024211 x = 0.210024211 Simplifying x = 0.210024211Subproblem 2
x + -0.0625 = -0.147524211 Simplifying x + -0.0625 = -0.147524211 Reorder the terms: -0.0625 + x = -0.147524211 Solving -0.0625 + x = -0.147524211 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 = -0.147524211 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -0.147524211 + 0.0625 x = -0.147524211 + 0.0625 Combine like terms: -0.147524211 + 0.0625 = -0.085024211 x = -0.085024211 Simplifying x = -0.085024211Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.210024211, -0.085024211}
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