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Simplifying x + x2 = 60.25 Solving x + x2 = 60.25 Solving for variable 'x'. Reorder the terms: -60.25 + x + x2 = 60.25 + -60.25 Combine like terms: 60.25 + -60.25 = 0.00 -60.25 + x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '60.25' to each side of the equation. -60.25 + x + 60.25 + x2 = 0.00 + 60.25 Reorder the terms: -60.25 + 60.25 + x + x2 = 0.00 + 60.25 Combine like terms: -60.25 + 60.25 = 0.00 0.00 + x + x2 = 0.00 + 60.25 x + x2 = 0.00 + 60.25 Combine like terms: 0.00 + 60.25 = 60.25 x + x2 = 60.25 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 60.25 + 0.25 Reorder the terms: 0.25 + x + x2 = 60.25 + 0.25 Combine like terms: 60.25 + 0.25 = 60.5 0.25 + x + x2 = 60.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 60.5 Calculate the square root of the right side: 7.778174593 Break this problem into two subproblems by setting (x + 0.5) equal to 7.778174593 and -7.778174593.Subproblem 1
x + 0.5 = 7.778174593 Simplifying x + 0.5 = 7.778174593 Reorder the terms: 0.5 + x = 7.778174593 Solving 0.5 + x = 7.778174593 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 7.778174593 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.778174593 + -0.5 x = 7.778174593 + -0.5 Combine like terms: 7.778174593 + -0.5 = 7.278174593 x = 7.278174593 Simplifying x = 7.278174593Subproblem 2
x + 0.5 = -7.778174593 Simplifying x + 0.5 = -7.778174593 Reorder the terms: 0.5 + x = -7.778174593 Solving 0.5 + x = -7.778174593 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -7.778174593 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.778174593 + -0.5 x = -7.778174593 + -0.5 Combine like terms: -7.778174593 + -0.5 = -8.278174593 x = -8.278174593 Simplifying x = -8.278174593Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.278174593, -8.278174593}
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