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Simplifying 62x2 + -128x + 64 = 9 Reorder the terms: 64 + -128x + 62x2 = 9 Solving 64 + -128x + 62x2 = 9 Solving for variable 'x'. Reorder the terms: 64 + -9 + -128x + 62x2 = 9 + -9 Combine like terms: 64 + -9 = 55 55 + -128x + 62x2 = 9 + -9 Combine like terms: 9 + -9 = 0 55 + -128x + 62x2 = 0 Begin completing the square. Divide all terms by 62 the coefficient of the squared term: Divide each side by '62'. 0.8870967742 + -2.064516129x + x2 = 0 Move the constant term to the right: Add '-0.8870967742' to each side of the equation. 0.8870967742 + -2.064516129x + -0.8870967742 + x2 = 0 + -0.8870967742 Reorder the terms: 0.8870967742 + -0.8870967742 + -2.064516129x + x2 = 0 + -0.8870967742 Combine like terms: 0.8870967742 + -0.8870967742 = 0.0000000000 0.0000000000 + -2.064516129x + x2 = 0 + -0.8870967742 -2.064516129x + x2 = 0 + -0.8870967742 Combine like terms: 0 + -0.8870967742 = -0.8870967742 -2.064516129x + x2 = -0.8870967742 The x term is -2.064516129x. Take half its coefficient (-1.032258065). Square it (1.065556713) and add it to both sides. Add '1.065556713' to each side of the equation. -2.064516129x + 1.065556713 + x2 = -0.8870967742 + 1.065556713 Reorder the terms: 1.065556713 + -2.064516129x + x2 = -0.8870967742 + 1.065556713 Combine like terms: -0.8870967742 + 1.065556713 = 0.1784599388 1.065556713 + -2.064516129x + x2 = 0.1784599388 Factor a perfect square on the left side: (x + -1.032258065)(x + -1.032258065) = 0.1784599388 Calculate the square root of the right side: 0.42244519 Break this problem into two subproblems by setting (x + -1.032258065) equal to 0.42244519 and -0.42244519.Subproblem 1
x + -1.032258065 = 0.42244519 Simplifying x + -1.032258065 = 0.42244519 Reorder the terms: -1.032258065 + x = 0.42244519 Solving -1.032258065 + x = 0.42244519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.032258065' to each side of the equation. -1.032258065 + 1.032258065 + x = 0.42244519 + 1.032258065 Combine like terms: -1.032258065 + 1.032258065 = 0.000000000 0.000000000 + x = 0.42244519 + 1.032258065 x = 0.42244519 + 1.032258065 Combine like terms: 0.42244519 + 1.032258065 = 1.454703255 x = 1.454703255 Simplifying x = 1.454703255Subproblem 2
x + -1.032258065 = -0.42244519 Simplifying x + -1.032258065 = -0.42244519 Reorder the terms: -1.032258065 + x = -0.42244519 Solving -1.032258065 + x = -0.42244519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.032258065' to each side of the equation. -1.032258065 + 1.032258065 + x = -0.42244519 + 1.032258065 Combine like terms: -1.032258065 + 1.032258065 = 0.000000000 0.000000000 + x = -0.42244519 + 1.032258065 x = -0.42244519 + 1.032258065 Combine like terms: -0.42244519 + 1.032258065 = 0.609812875 x = 0.609812875 Simplifying x = 0.609812875Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.454703255, 0.609812875}
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