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Simplifying x2 + 5x = 250 Reorder the terms: 5x + x2 = 250 Solving 5x + x2 = 250 Solving for variable 'x'. Reorder the terms: -250 + 5x + x2 = 250 + -250 Combine like terms: 250 + -250 = 0 -250 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '250' to each side of the equation. -250 + 5x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + 5x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + 5x + x2 = 0 + 250 5x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 5x + x2 = 250 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 250 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 250 + 6.25 Combine like terms: 250 + 6.25 = 256.25 6.25 + 5x + x2 = 256.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 256.25 Calculate the square root of the right side: 16.007810594 Break this problem into two subproblems by setting (x + 2.5) equal to 16.007810594 and -16.007810594.Subproblem 1
x + 2.5 = 16.007810594 Simplifying x + 2.5 = 16.007810594 Reorder the terms: 2.5 + x = 16.007810594 Solving 2.5 + x = 16.007810594 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 16.007810594 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 16.007810594 + -2.5 x = 16.007810594 + -2.5 Combine like terms: 16.007810594 + -2.5 = 13.507810594 x = 13.507810594 Simplifying x = 13.507810594Subproblem 2
x + 2.5 = -16.007810594 Simplifying x + 2.5 = -16.007810594 Reorder the terms: 2.5 + x = -16.007810594 Solving 2.5 + x = -16.007810594 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -16.007810594 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -16.007810594 + -2.5 x = -16.007810594 + -2.5 Combine like terms: -16.007810594 + -2.5 = -18.507810594 x = -18.507810594 Simplifying x = -18.507810594Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.507810594, -18.507810594}
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