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Simplifying x2 + 55x = 250 Reorder the terms: 55x + x2 = 250 Solving 55x + x2 = 250 Solving for variable 'x'. Reorder the terms: -250 + 55x + x2 = 250 + -250 Combine like terms: 250 + -250 = 0 -250 + 55x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '250' to each side of the equation. -250 + 55x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + 55x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + 55x + x2 = 0 + 250 55x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 55x + x2 = 250 The x term is 55x. Take half its coefficient (27.5). Square it (756.25) and add it to both sides. Add '756.25' to each side of the equation. 55x + 756.25 + x2 = 250 + 756.25 Reorder the terms: 756.25 + 55x + x2 = 250 + 756.25 Combine like terms: 250 + 756.25 = 1006.25 756.25 + 55x + x2 = 1006.25 Factor a perfect square on the left side: (x + 27.5)(x + 27.5) = 1006.25 Calculate the square root of the right side: 31.721443851 Break this problem into two subproblems by setting (x + 27.5) equal to 31.721443851 and -31.721443851.Subproblem 1
x + 27.5 = 31.721443851 Simplifying x + 27.5 = 31.721443851 Reorder the terms: 27.5 + x = 31.721443851 Solving 27.5 + x = 31.721443851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + x = 31.721443851 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = 31.721443851 + -27.5 x = 31.721443851 + -27.5 Combine like terms: 31.721443851 + -27.5 = 4.221443851 x = 4.221443851 Simplifying x = 4.221443851Subproblem 2
x + 27.5 = -31.721443851 Simplifying x + 27.5 = -31.721443851 Reorder the terms: 27.5 + x = -31.721443851 Solving 27.5 + x = -31.721443851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + x = -31.721443851 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = -31.721443851 + -27.5 x = -31.721443851 + -27.5 Combine like terms: -31.721443851 + -27.5 = -59.221443851 x = -59.221443851 Simplifying x = -59.221443851Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.221443851, -59.221443851}
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