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Simplifying 64x2 + -48x + 7 = 0 Reorder the terms: 7 + -48x + 64x2 = 0 Solving 7 + -48x + 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'. 0.109375 + -0.75x + x2 = 0 Move the constant term to the right: Add '-0.109375' to each side of the equation. 0.109375 + -0.75x + -0.109375 + x2 = 0 + -0.109375 Reorder the terms: 0.109375 + -0.109375 + -0.75x + x2 = 0 + -0.109375 Combine like terms: 0.109375 + -0.109375 = 0.000000 0.000000 + -0.75x + x2 = 0 + -0.109375 -0.75x + x2 = 0 + -0.109375 Combine like terms: 0 + -0.109375 = -0.109375 -0.75x + x2 = -0.109375 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = -0.109375 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = -0.109375 + 0.140625 Combine like terms: -0.109375 + 0.140625 = 0.03125 0.140625 + -0.75x + x2 = 0.03125 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 0.03125 Calculate the square root of the right side: 0.176776695 Break this problem into two subproblems by setting (x + -0.375) equal to 0.176776695 and -0.176776695.Subproblem 1
x + -0.375 = 0.176776695 Simplifying x + -0.375 = 0.176776695 Reorder the terms: -0.375 + x = 0.176776695 Solving -0.375 + x = 0.176776695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 0.176776695 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 0.176776695 + 0.375 x = 0.176776695 + 0.375 Combine like terms: 0.176776695 + 0.375 = 0.551776695 x = 0.551776695 Simplifying x = 0.551776695Subproblem 2
x + -0.375 = -0.176776695 Simplifying x + -0.375 = -0.176776695 Reorder the terms: -0.375 + x = -0.176776695 Solving -0.375 + x = -0.176776695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -0.176776695 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -0.176776695 + 0.375 x = -0.176776695 + 0.375 Combine like terms: -0.176776695 + 0.375 = 0.198223305 x = 0.198223305 Simplifying x = 0.198223305Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.551776695, 0.198223305}
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