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Simplifying x2 + 9x = 240 Reorder the terms: 9x + x2 = 240 Solving 9x + x2 = 240 Solving for variable 'x'. Reorder the terms: -240 + 9x + x2 = 240 + -240 Combine like terms: 240 + -240 = 0 -240 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + 9x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + 9x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 9x + x2 = 0 + 240 9x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 9x + x2 = 240 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 = 240 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 240 + 20.25 Combine like terms: 240 + 20.25 = 260.25 20.25 + 9x + x2 = 260.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 260.25 Calculate the square root of the right side: 16.132265805 Break this problem into two subproblems by setting (x + 4.5) equal to 16.132265805 and -16.132265805.Subproblem 1
x + 4.5 = 16.132265805 Simplifying x + 4.5 = 16.132265805 Reorder the terms: 4.5 + x = 16.132265805 Solving 4.5 + x = 16.132265805 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 = 16.132265805 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 16.132265805 + -4.5 x = 16.132265805 + -4.5 Combine like terms: 16.132265805 + -4.5 = 11.632265805 x = 11.632265805 Simplifying x = 11.632265805Subproblem 2
x + 4.5 = -16.132265805 Simplifying x + 4.5 = -16.132265805 Reorder the terms: 4.5 + x = -16.132265805 Solving 4.5 + x = -16.132265805 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 = -16.132265805 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -16.132265805 + -4.5 x = -16.132265805 + -4.5 Combine like terms: -16.132265805 + -4.5 = -20.632265805 x = -20.632265805 Simplifying x = -20.632265805Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.632265805, -20.632265805}
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