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Simplifying x2 + 9x = 250 Reorder the terms: 9x + x2 = 250 Solving 9x + x2 = 250 Solving for variable 'x'. Reorder the terms: -250 + 9x + x2 = 250 + -250 Combine like terms: 250 + -250 = 0 -250 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '250' to each side of the equation. -250 + 9x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + 9x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + 9x + x2 = 0 + 250 9x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 9x + x2 = 250 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 250 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 250 + 20.25 Combine like terms: 250 + 20.25 = 270.25 20.25 + 9x + x2 = 270.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 270.25 Calculate the square root of the right side: 16.439282223 Break this problem into two subproblems by setting (x + 4.5) equal to 16.439282223 and -16.439282223.Subproblem 1
x + 4.5 = 16.439282223 Simplifying x + 4.5 = 16.439282223 Reorder the terms: 4.5 + x = 16.439282223 Solving 4.5 + x = 16.439282223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 16.439282223 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 16.439282223 + -4.5 x = 16.439282223 + -4.5 Combine like terms: 16.439282223 + -4.5 = 11.939282223 x = 11.939282223 Simplifying x = 11.939282223Subproblem 2
x + 4.5 = -16.439282223 Simplifying x + 4.5 = -16.439282223 Reorder the terms: 4.5 + x = -16.439282223 Solving 4.5 + x = -16.439282223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -16.439282223 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -16.439282223 + -4.5 x = -16.439282223 + -4.5 Combine like terms: -16.439282223 + -4.5 = -20.939282223 x = -20.939282223 Simplifying x = -20.939282223Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.939282223, -20.939282223}
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