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Simplifying 64x2 + 16x = 1 Reorder the terms: 16x + 64x2 = 1 Solving 16x + 64x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 16x + 64x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 16x + 64x2 = 0 Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.015625 + 0.25x + x2 = 0 Move the constant term to the right: Add '0.015625' to each side of the equation. -0.015625 + 0.25x + 0.015625 + x2 = 0 + 0.015625 Reorder the terms: -0.015625 + 0.015625 + 0.25x + x2 = 0 + 0.015625 Combine like terms: -0.015625 + 0.015625 = 0.000000 0.000000 + 0.25x + x2 = 0 + 0.015625 0.25x + x2 = 0 + 0.015625 Combine like terms: 0 + 0.015625 = 0.015625 0.25x + x2 = 0.015625 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 0.015625 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 0.015625 + 0.015625 Combine like terms: 0.015625 + 0.015625 = 0.03125 0.015625 + 0.25x + x2 = 0.03125 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 0.03125 Calculate the square root of the right side: 0.176776695 Break this problem into two subproblems by setting (x + 0.125) equal to 0.176776695 and -0.176776695.Subproblem 1
x + 0.125 = 0.176776695 Simplifying x + 0.125 = 0.176776695 Reorder the terms: 0.125 + x = 0.176776695 Solving 0.125 + x = 0.176776695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 0.176776695 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 0.176776695 + -0.125 x = 0.176776695 + -0.125 Combine like terms: 0.176776695 + -0.125 = 0.051776695 x = 0.051776695 Simplifying x = 0.051776695Subproblem 2
x + 0.125 = -0.176776695 Simplifying x + 0.125 = -0.176776695 Reorder the terms: 0.125 + x = -0.176776695 Solving 0.125 + x = -0.176776695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -0.176776695 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -0.176776695 + -0.125 x = -0.176776695 + -0.125 Combine like terms: -0.176776695 + -0.125 = -0.301776695 x = -0.301776695 Simplifying x = -0.301776695Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.051776695, -0.301776695}
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