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Simplifying x2 + 9x + -120 = 0 Reorder the terms: -120 + 9x + x2 = 0 Solving -120 + 9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '120' to each side of the equation. -120 + 9x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 9x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 9x + x2 = 0 + 120 9x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 9x + x2 = 120 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 = 120 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 120 + 20.25 Combine like terms: 120 + 20.25 = 140.25 20.25 + 9x + x2 = 140.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 140.25 Calculate the square root of the right side: 11.842719282 Break this problem into two subproblems by setting (x + 4.5) equal to 11.842719282 and -11.842719282.Subproblem 1
x + 4.5 = 11.842719282 Simplifying x + 4.5 = 11.842719282 Reorder the terms: 4.5 + x = 11.842719282 Solving 4.5 + x = 11.842719282 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 = 11.842719282 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 11.842719282 + -4.5 x = 11.842719282 + -4.5 Combine like terms: 11.842719282 + -4.5 = 7.342719282 x = 7.342719282 Simplifying x = 7.342719282Subproblem 2
x + 4.5 = -11.842719282 Simplifying x + 4.5 = -11.842719282 Reorder the terms: 4.5 + x = -11.842719282 Solving 4.5 + x = -11.842719282 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 = -11.842719282 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -11.842719282 + -4.5 x = -11.842719282 + -4.5 Combine like terms: -11.842719282 + -4.5 = -16.342719282 x = -16.342719282 Simplifying x = -16.342719282Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.342719282, -16.342719282}
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