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Simplifying 64x2 + 8x + -81 = 0 Reorder the terms: -81 + 8x + 64x2 = 0 Solving -81 + 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'. -1.265625 + 0.125x + x2 = 0 Move the constant term to the right: Add '1.265625' to each side of the equation. -1.265625 + 0.125x + 1.265625 + x2 = 0 + 1.265625 Reorder the terms: -1.265625 + 1.265625 + 0.125x + x2 = 0 + 1.265625 Combine like terms: -1.265625 + 1.265625 = 0.000000 0.000000 + 0.125x + x2 = 0 + 1.265625 0.125x + x2 = 0 + 1.265625 Combine like terms: 0 + 1.265625 = 1.265625 0.125x + x2 = 1.265625 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 = 1.265625 + 0.00390625 Reorder the terms: 0.00390625 + 0.125x + x2 = 1.265625 + 0.00390625 Combine like terms: 1.265625 + 0.00390625 = 1.26953125 0.00390625 + 0.125x + x2 = 1.26953125 Factor a perfect square on the left side: (x + 0.0625)(x + 0.0625) = 1.26953125 Calculate the square root of the right side: 1.126734774 Break this problem into two subproblems by setting (x + 0.0625) equal to 1.126734774 and -1.126734774.Subproblem 1
x + 0.0625 = 1.126734774 Simplifying x + 0.0625 = 1.126734774 Reorder the terms: 0.0625 + x = 1.126734774 Solving 0.0625 + x = 1.126734774 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 = 1.126734774 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = 1.126734774 + -0.0625 x = 1.126734774 + -0.0625 Combine like terms: 1.126734774 + -0.0625 = 1.064234774 x = 1.064234774 Simplifying x = 1.064234774Subproblem 2
x + 0.0625 = -1.126734774 Simplifying x + 0.0625 = -1.126734774 Reorder the terms: 0.0625 + x = -1.126734774 Solving 0.0625 + x = -1.126734774 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 = -1.126734774 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = -1.126734774 + -0.0625 x = -1.126734774 + -0.0625 Combine like terms: -1.126734774 + -0.0625 = -1.189234774 x = -1.189234774 Simplifying x = -1.189234774Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.064234774, -1.189234774}
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