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Simplifying x2 + 11x = 250 Reorder the terms: 11x + x2 = 250 Solving 11x + x2 = 250 Solving for variable 'x'. Reorder the terms: -250 + 11x + x2 = 250 + -250 Combine like terms: 250 + -250 = 0 -250 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '250' to each side of the equation. -250 + 11x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + 11x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + 11x + x2 = 0 + 250 11x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 11x + x2 = 250 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 250 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 250 + 30.25 Combine like terms: 250 + 30.25 = 280.25 30.25 + 11x + x2 = 280.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 280.25 Calculate the square root of the right side: 16.740669043 Break this problem into two subproblems by setting (x + 5.5) equal to 16.740669043 and -16.740669043.Subproblem 1
x + 5.5 = 16.740669043 Simplifying x + 5.5 = 16.740669043 Reorder the terms: 5.5 + x = 16.740669043 Solving 5.5 + x = 16.740669043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 16.740669043 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 16.740669043 + -5.5 x = 16.740669043 + -5.5 Combine like terms: 16.740669043 + -5.5 = 11.240669043 x = 11.240669043 Simplifying x = 11.240669043Subproblem 2
x + 5.5 = -16.740669043 Simplifying x + 5.5 = -16.740669043 Reorder the terms: 5.5 + x = -16.740669043 Solving 5.5 + x = -16.740669043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -16.740669043 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -16.740669043 + -5.5 x = -16.740669043 + -5.5 Combine like terms: -16.740669043 + -5.5 = -22.240669043 x = -22.240669043 Simplifying x = -22.240669043Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.240669043, -22.240669043}
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