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Simplifying -4x2 + 64 = x Reorder the terms: 64 + -4x2 = x Solving 64 + -4x2 = x Solving for variable 'x'. Reorder the terms: 64 + -1x + -4x2 = x + -1x Combine like terms: x + -1x = 0 64 + -1x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -16 + 0.25x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 0.25x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 0.25x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 0.25x + x2 = 0 + 16 0.25x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 0.25x + x2 = 16 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 = 16 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 16 + 0.015625 Combine like terms: 16 + 0.015625 = 16.015625 0.015625 + 0.25x + x2 = 16.015625 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 16.015625 Calculate the square root of the right side: 4.001952648 Break this problem into two subproblems by setting (x + 0.125) equal to 4.001952648 and -4.001952648.Subproblem 1
x + 0.125 = 4.001952648 Simplifying x + 0.125 = 4.001952648 Reorder the terms: 0.125 + x = 4.001952648 Solving 0.125 + x = 4.001952648 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 = 4.001952648 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 4.001952648 + -0.125 x = 4.001952648 + -0.125 Combine like terms: 4.001952648 + -0.125 = 3.876952648 x = 3.876952648 Simplifying x = 3.876952648Subproblem 2
x + 0.125 = -4.001952648 Simplifying x + 0.125 = -4.001952648 Reorder the terms: 0.125 + x = -4.001952648 Solving 0.125 + x = -4.001952648 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 = -4.001952648 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -4.001952648 + -0.125 x = -4.001952648 + -0.125 Combine like terms: -4.001952648 + -0.125 = -4.126952648 x = -4.126952648 Simplifying x = -4.126952648Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.876952648, -4.126952648}
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