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Simplifying 64x2 + -116x + 9 = 0 Reorder the terms: 9 + -116x + 64x2 = 0 Solving 9 + -116x + 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 + -1.8125x + x2 = 0 Move the constant term to the right: Add '-0.140625' to each side of the equation. 0.140625 + -1.8125x + -0.140625 + x2 = 0 + -0.140625 Reorder the terms: 0.140625 + -0.140625 + -1.8125x + x2 = 0 + -0.140625 Combine like terms: 0.140625 + -0.140625 = 0.000000 0.000000 + -1.8125x + x2 = 0 + -0.140625 -1.8125x + x2 = 0 + -0.140625 Combine like terms: 0 + -0.140625 = -0.140625 -1.8125x + x2 = -0.140625 The x term is -1.8125x. Take half its coefficient (-0.90625). Square it (0.8212890625) and add it to both sides. Add '0.8212890625' to each side of the equation. -1.8125x + 0.8212890625 + x2 = -0.140625 + 0.8212890625 Reorder the terms: 0.8212890625 + -1.8125x + x2 = -0.140625 + 0.8212890625 Combine like terms: -0.140625 + 0.8212890625 = 0.6806640625 0.8212890625 + -1.8125x + x2 = 0.6806640625 Factor a perfect square on the left side: (x + -0.90625)(x + -0.90625) = 0.6806640625 Calculate the square root of the right side: 0.825023674 Break this problem into two subproblems by setting (x + -0.90625) equal to 0.825023674 and -0.825023674.Subproblem 1
x + -0.90625 = 0.825023674 Simplifying x + -0.90625 = 0.825023674 Reorder the terms: -0.90625 + x = 0.825023674 Solving -0.90625 + x = 0.825023674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.90625' to each side of the equation. -0.90625 + 0.90625 + x = 0.825023674 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + x = 0.825023674 + 0.90625 x = 0.825023674 + 0.90625 Combine like terms: 0.825023674 + 0.90625 = 1.731273674 x = 1.731273674 Simplifying x = 1.731273674Subproblem 2
x + -0.90625 = -0.825023674 Simplifying x + -0.90625 = -0.825023674 Reorder the terms: -0.90625 + x = -0.825023674 Solving -0.90625 + x = -0.825023674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.90625' to each side of the equation. -0.90625 + 0.90625 + x = -0.825023674 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + x = -0.825023674 + 0.90625 x = -0.825023674 + 0.90625 Combine like terms: -0.825023674 + 0.90625 = 0.081226326 x = 0.081226326 Simplifying x = 0.081226326Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.731273674, 0.081226326}
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