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Simplifying 8x2 + -1x + -506 = 0 Reorder the terms: -506 + -1x + 8x2 = 0 Solving -506 + -1x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -63.25 + -0.125x + x2 = 0 Move the constant term to the right: Add '63.25' to each side of the equation. -63.25 + -0.125x + 63.25 + x2 = 0 + 63.25 Reorder the terms: -63.25 + 63.25 + -0.125x + x2 = 0 + 63.25 Combine like terms: -63.25 + 63.25 = 0.00 0.00 + -0.125x + x2 = 0 + 63.25 -0.125x + x2 = 0 + 63.25 Combine like terms: 0 + 63.25 = 63.25 -0.125x + x2 = 63.25 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 = 63.25 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 63.25 + 0.00390625 Combine like terms: 63.25 + 0.00390625 = 63.25390625 0.00390625 + -0.125x + x2 = 63.25390625 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 63.25390625 Calculate the square root of the right side: 7.95323244 Break this problem into two subproblems by setting (x + -0.0625) equal to 7.95323244 and -7.95323244.Subproblem 1
x + -0.0625 = 7.95323244 Simplifying x + -0.0625 = 7.95323244 Reorder the terms: -0.0625 + x = 7.95323244 Solving -0.0625 + x = 7.95323244 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 = 7.95323244 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 7.95323244 + 0.0625 x = 7.95323244 + 0.0625 Combine like terms: 7.95323244 + 0.0625 = 8.01573244 x = 8.01573244 Simplifying x = 8.01573244Subproblem 2
x + -0.0625 = -7.95323244 Simplifying x + -0.0625 = -7.95323244 Reorder the terms: -0.0625 + x = -7.95323244 Solving -0.0625 + x = -7.95323244 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 = -7.95323244 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -7.95323244 + 0.0625 x = -7.95323244 + 0.0625 Combine like terms: -7.95323244 + 0.0625 = -7.89073244 x = -7.89073244 Simplifying x = -7.89073244Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.01573244, -7.89073244}
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