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Simplifying x2 + 0.25x = 63 Reorder the terms: 0.25x + x2 = 63 Solving 0.25x + x2 = 63 Solving for variable 'x'. Reorder the terms: -63 + 0.25x + x2 = 63 + -63 Combine like terms: 63 + -63 = 0 -63 + 0.25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + 0.25x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + 0.25x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 0.25x + x2 = 0 + 63 0.25x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 0.25x + x2 = 63 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 = 63 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 63 + 0.015625 Combine like terms: 63 + 0.015625 = 63.015625 0.015625 + 0.25x + x2 = 63.015625 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 63.015625 Calculate the square root of the right side: 7.938238155 Break this problem into two subproblems by setting (x + 0.125) equal to 7.938238155 and -7.938238155.Subproblem 1
x + 0.125 = 7.938238155 Simplifying x + 0.125 = 7.938238155 Reorder the terms: 0.125 + x = 7.938238155 Solving 0.125 + x = 7.938238155 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 = 7.938238155 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 7.938238155 + -0.125 x = 7.938238155 + -0.125 Combine like terms: 7.938238155 + -0.125 = 7.813238155 x = 7.813238155 Simplifying x = 7.813238155Subproblem 2
x + 0.125 = -7.938238155 Simplifying x + 0.125 = -7.938238155 Reorder the terms: 0.125 + x = -7.938238155 Solving 0.125 + x = -7.938238155 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 = -7.938238155 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -7.938238155 + -0.125 x = -7.938238155 + -0.125 Combine like terms: -7.938238155 + -0.125 = -8.063238155 x = -8.063238155 Simplifying x = -8.063238155Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.813238155, -8.063238155}
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