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Simplifying 64x2 + -24x + -9 = 0 Reorder the terms: -9 + -24x + 64x2 = 0 Solving -9 + -24x + 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 + -0.375x + x2 = 0 Move the constant term to the right: Add '0.140625' to each side of the equation. -0.140625 + -0.375x + 0.140625 + x2 = 0 + 0.140625 Reorder the terms: -0.140625 + 0.140625 + -0.375x + x2 = 0 + 0.140625 Combine like terms: -0.140625 + 0.140625 = 0.000000 0.000000 + -0.375x + x2 = 0 + 0.140625 -0.375x + x2 = 0 + 0.140625 Combine like terms: 0 + 0.140625 = 0.140625 -0.375x + x2 = 0.140625 The x term is -0.375x. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375x + 0.03515625 + x2 = 0.140625 + 0.03515625 Reorder the terms: 0.03515625 + -0.375x + x2 = 0.140625 + 0.03515625 Combine like terms: 0.140625 + 0.03515625 = 0.17578125 0.03515625 + -0.375x + x2 = 0.17578125 Factor a perfect square on the left side: (x + -0.1875)(x + -0.1875) = 0.17578125 Calculate the square root of the right side: 0.419262746 Break this problem into two subproblems by setting (x + -0.1875) equal to 0.419262746 and -0.419262746.Subproblem 1
x + -0.1875 = 0.419262746 Simplifying x + -0.1875 = 0.419262746 Reorder the terms: -0.1875 + x = 0.419262746 Solving -0.1875 + x = 0.419262746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = 0.419262746 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = 0.419262746 + 0.1875 x = 0.419262746 + 0.1875 Combine like terms: 0.419262746 + 0.1875 = 0.606762746 x = 0.606762746 Simplifying x = 0.606762746Subproblem 2
x + -0.1875 = -0.419262746 Simplifying x + -0.1875 = -0.419262746 Reorder the terms: -0.1875 + x = -0.419262746 Solving -0.1875 + x = -0.419262746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = -0.419262746 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = -0.419262746 + 0.1875 x = -0.419262746 + 0.1875 Combine like terms: -0.419262746 + 0.1875 = -0.231762746 x = -0.231762746 Simplifying x = -0.231762746Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.606762746, -0.231762746}
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