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Simplifying 64x2 + -48x = 39 Reorder the terms: -48x + 64x2 = 39 Solving -48x + 64x2 = 39 Solving for variable 'x'. Reorder the terms: -39 + -48x + 64x2 = 39 + -39 Combine like terms: 39 + -39 = 0 -39 + -48x + 64x2 = 0 Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.609375 + -0.75x + x2 = 0 Move the constant term to the right: Add '0.609375' to each side of the equation. -0.609375 + -0.75x + 0.609375 + x2 = 0 + 0.609375 Reorder the terms: -0.609375 + 0.609375 + -0.75x + x2 = 0 + 0.609375 Combine like terms: -0.609375 + 0.609375 = 0.000000 0.000000 + -0.75x + x2 = 0 + 0.609375 -0.75x + x2 = 0 + 0.609375 Combine like terms: 0 + 0.609375 = 0.609375 -0.75x + x2 = 0.609375 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 = 0.609375 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 0.609375 + 0.140625 Combine like terms: 0.609375 + 0.140625 = 0.75 0.140625 + -0.75x + x2 = 0.75 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 0.75 Calculate the square root of the right side: 0.866025404 Break this problem into two subproblems by setting (x + -0.375) equal to 0.866025404 and -0.866025404.Subproblem 1
x + -0.375 = 0.866025404 Simplifying x + -0.375 = 0.866025404 Reorder the terms: -0.375 + x = 0.866025404 Solving -0.375 + x = 0.866025404 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 = 0.866025404 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 0.866025404 + 0.375 x = 0.866025404 + 0.375 Combine like terms: 0.866025404 + 0.375 = 1.241025404 x = 1.241025404 Simplifying x = 1.241025404Subproblem 2
x + -0.375 = -0.866025404 Simplifying x + -0.375 = -0.866025404 Reorder the terms: -0.375 + x = -0.866025404 Solving -0.375 + x = -0.866025404 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 = -0.866025404 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -0.866025404 + 0.375 x = -0.866025404 + 0.375 Combine like terms: -0.866025404 + 0.375 = -0.491025404 x = -0.491025404 Simplifying x = -0.491025404Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.241025404, -0.491025404}
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