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Simplifying 64x2 + -69x + -2 = 0 Reorder the terms: -2 + -69x + 64x2 = 0 Solving -2 + -69x + 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'. -0.03125 + -1.078125x + x2 = 0 Move the constant term to the right: Add '0.03125' to each side of the equation. -0.03125 + -1.078125x + 0.03125 + x2 = 0 + 0.03125 Reorder the terms: -0.03125 + 0.03125 + -1.078125x + x2 = 0 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + -1.078125x + x2 = 0 + 0.03125 -1.078125x + x2 = 0 + 0.03125 Combine like terms: 0 + 0.03125 = 0.03125 -1.078125x + x2 = 0.03125 The x term is -1.078125x. Take half its coefficient (-0.5390625). Square it (0.2905883789) and add it to both sides. Add '0.2905883789' to each side of the equation. -1.078125x + 0.2905883789 + x2 = 0.03125 + 0.2905883789 Reorder the terms: 0.2905883789 + -1.078125x + x2 = 0.03125 + 0.2905883789 Combine like terms: 0.03125 + 0.2905883789 = 0.3218383789 0.2905883789 + -1.078125x + x2 = 0.3218383789 Factor a perfect square on the left side: (x + -0.5390625)(x + -0.5390625) = 0.3218383789 Calculate the square root of the right side: 0.567308011 Break this problem into two subproblems by setting (x + -0.5390625) equal to 0.567308011 and -0.567308011.Subproblem 1
x + -0.5390625 = 0.567308011 Simplifying x + -0.5390625 = 0.567308011 Reorder the terms: -0.5390625 + x = 0.567308011 Solving -0.5390625 + x = 0.567308011 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5390625' to each side of the equation. -0.5390625 + 0.5390625 + x = 0.567308011 + 0.5390625 Combine like terms: -0.5390625 + 0.5390625 = 0.0000000 0.0000000 + x = 0.567308011 + 0.5390625 x = 0.567308011 + 0.5390625 Combine like terms: 0.567308011 + 0.5390625 = 1.106370511 x = 1.106370511 Simplifying x = 1.106370511Subproblem 2
x + -0.5390625 = -0.567308011 Simplifying x + -0.5390625 = -0.567308011 Reorder the terms: -0.5390625 + x = -0.567308011 Solving -0.5390625 + x = -0.567308011 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5390625' to each side of the equation. -0.5390625 + 0.5390625 + x = -0.567308011 + 0.5390625 Combine like terms: -0.5390625 + 0.5390625 = 0.0000000 0.0000000 + x = -0.567308011 + 0.5390625 x = -0.567308011 + 0.5390625 Combine like terms: -0.567308011 + 0.5390625 = -0.028245511 x = -0.028245511 Simplifying x = -0.028245511Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.106370511, -0.028245511}
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