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Simplifying 64x2 + 9x + -9 = 0 Reorder the terms: -9 + 9x + 64x2 = 0 Solving -9 + 9x + 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'. -0.140625 + 0.140625x + x2 = 0 Move the constant term to the right: Add '0.140625' to each side of the equation. -0.140625 + 0.140625x + 0.140625 + x2 = 0 + 0.140625 Reorder the terms: -0.140625 + 0.140625 + 0.140625x + x2 = 0 + 0.140625 Combine like terms: -0.140625 + 0.140625 = 0.000000 0.000000 + 0.140625x + x2 = 0 + 0.140625 0.140625x + x2 = 0 + 0.140625 Combine like terms: 0 + 0.140625 = 0.140625 0.140625x + x2 = 0.140625 The x term is 0.140625x. Take half its coefficient (0.0703125). Square it (0.004943847656) and add it to both sides. Add '0.004943847656' to each side of the equation. 0.140625x + 0.004943847656 + x2 = 0.140625 + 0.004943847656 Reorder the terms: 0.004943847656 + 0.140625x + x2 = 0.140625 + 0.004943847656 Combine like terms: 0.140625 + 0.004943847656 = 0.145568847656 0.004943847656 + 0.140625x + x2 = 0.145568847656 Factor a perfect square on the left side: (x + 0.0703125)(x + 0.0703125) = 0.145568847656 Calculate the square root of the right side: 0.381534858 Break this problem into two subproblems by setting (x + 0.0703125) equal to 0.381534858 and -0.381534858.Subproblem 1
x + 0.0703125 = 0.381534858 Simplifying x + 0.0703125 = 0.381534858 Reorder the terms: 0.0703125 + x = 0.381534858 Solving 0.0703125 + x = 0.381534858 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0703125' to each side of the equation. 0.0703125 + -0.0703125 + x = 0.381534858 + -0.0703125 Combine like terms: 0.0703125 + -0.0703125 = 0.0000000 0.0000000 + x = 0.381534858 + -0.0703125 x = 0.381534858 + -0.0703125 Combine like terms: 0.381534858 + -0.0703125 = 0.311222358 x = 0.311222358 Simplifying x = 0.311222358Subproblem 2
x + 0.0703125 = -0.381534858 Simplifying x + 0.0703125 = -0.381534858 Reorder the terms: 0.0703125 + x = -0.381534858 Solving 0.0703125 + x = -0.381534858 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0703125' to each side of the equation. 0.0703125 + -0.0703125 + x = -0.381534858 + -0.0703125 Combine like terms: 0.0703125 + -0.0703125 = 0.0000000 0.0000000 + x = -0.381534858 + -0.0703125 x = -0.381534858 + -0.0703125 Combine like terms: -0.381534858 + -0.0703125 = -0.451847358 x = -0.451847358 Simplifying x = -0.451847358Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.311222358, -0.451847358}
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