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Simplifying 64x2 + -5x + -11 = 0 Reorder the terms: -11 + -5x + 64x2 = 0 Solving -11 + -5x + 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'. -0.171875 + -0.078125x + x2 = 0 Move the constant term to the right: Add '0.171875' to each side of the equation. -0.171875 + -0.078125x + 0.171875 + x2 = 0 + 0.171875 Reorder the terms: -0.171875 + 0.171875 + -0.078125x + x2 = 0 + 0.171875 Combine like terms: -0.171875 + 0.171875 = 0.000000 0.000000 + -0.078125x + x2 = 0 + 0.171875 -0.078125x + x2 = 0 + 0.171875 Combine like terms: 0 + 0.171875 = 0.171875 -0.078125x + x2 = 0.171875 The x term is -0.078125x. Take half its coefficient (-0.0390625). Square it (0.001525878906) and add it to both sides. Add '0.001525878906' to each side of the equation. -0.078125x + 0.001525878906 + x2 = 0.171875 + 0.001525878906 Reorder the terms: 0.001525878906 + -0.078125x + x2 = 0.171875 + 0.001525878906 Combine like terms: 0.171875 + 0.001525878906 = 0.173400878906 0.001525878906 + -0.078125x + x2 = 0.173400878906 Factor a perfect square on the left side: (x + -0.0390625)(x + -0.0390625) = 0.173400878906 Calculate the square root of the right side: 0.416414312 Break this problem into two subproblems by setting (x + -0.0390625) equal to 0.416414312 and -0.416414312.Subproblem 1
x + -0.0390625 = 0.416414312 Simplifying x + -0.0390625 = 0.416414312 Reorder the terms: -0.0390625 + x = 0.416414312 Solving -0.0390625 + x = 0.416414312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0390625' to each side of the equation. -0.0390625 + 0.0390625 + x = 0.416414312 + 0.0390625 Combine like terms: -0.0390625 + 0.0390625 = 0.0000000 0.0000000 + x = 0.416414312 + 0.0390625 x = 0.416414312 + 0.0390625 Combine like terms: 0.416414312 + 0.0390625 = 0.455476812 x = 0.455476812 Simplifying x = 0.455476812Subproblem 2
x + -0.0390625 = -0.416414312 Simplifying x + -0.0390625 = -0.416414312 Reorder the terms: -0.0390625 + x = -0.416414312 Solving -0.0390625 + x = -0.416414312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0390625' to each side of the equation. -0.0390625 + 0.0390625 + x = -0.416414312 + 0.0390625 Combine like terms: -0.0390625 + 0.0390625 = 0.0000000 0.0000000 + x = -0.416414312 + 0.0390625 x = -0.416414312 + 0.0390625 Combine like terms: -0.416414312 + 0.0390625 = -0.377351812 x = -0.377351812 Simplifying x = -0.377351812Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.455476812, -0.377351812}
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