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Simplifying x2 + 45x + 120 = 0 Reorder the terms: 120 + 45x + x2 = 0 Solving 120 + 45x + 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 + 45x + -120 + x2 = 0 + -120 Reorder the terms: 120 + -120 + 45x + x2 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + 45x + x2 = 0 + -120 45x + x2 = 0 + -120 Combine like terms: 0 + -120 = -120 45x + x2 = -120 The x term is 45x. Take half its coefficient (22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. 45x + 506.25 + x2 = -120 + 506.25 Reorder the terms: 506.25 + 45x + x2 = -120 + 506.25 Combine like terms: -120 + 506.25 = 386.25 506.25 + 45x + x2 = 386.25 Factor a perfect square on the left side: (x + 22.5)(x + 22.5) = 386.25 Calculate the square root of the right side: 19.653244007 Break this problem into two subproblems by setting (x + 22.5) equal to 19.653244007 and -19.653244007.Subproblem 1
x + 22.5 = 19.653244007 Simplifying x + 22.5 = 19.653244007 Reorder the terms: 22.5 + x = 19.653244007 Solving 22.5 + x = 19.653244007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.5' to each side of the equation. 22.5 + -22.5 + x = 19.653244007 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = 19.653244007 + -22.5 x = 19.653244007 + -22.5 Combine like terms: 19.653244007 + -22.5 = -2.846755993 x = -2.846755993 Simplifying x = -2.846755993Subproblem 2
x + 22.5 = -19.653244007 Simplifying x + 22.5 = -19.653244007 Reorder the terms: 22.5 + x = -19.653244007 Solving 22.5 + x = -19.653244007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.5' to each side of the equation. 22.5 + -22.5 + x = -19.653244007 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = -19.653244007 + -22.5 x = -19.653244007 + -22.5 Combine like terms: -19.653244007 + -22.5 = -42.153244007 x = -42.153244007 Simplifying x = -42.153244007Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.846755993, -42.153244007}
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