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Simplifying n2 + 9n + -30 = 0 Reorder the terms: -30 + 9n + n2 = 0 Solving -30 + 9n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 9n + 30 + n2 = 0 + 30 Reorder the terms: -30 + 30 + 9n + n2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 9n + n2 = 0 + 30 9n + n2 = 0 + 30 Combine like terms: 0 + 30 = 30 9n + n2 = 30 The n term is 9n. 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. 9n + 20.25 + n2 = 30 + 20.25 Reorder the terms: 20.25 + 9n + n2 = 30 + 20.25 Combine like terms: 30 + 20.25 = 50.25 20.25 + 9n + n2 = 50.25 Factor a perfect square on the left side: (n + 4.5)(n + 4.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (n + 4.5) equal to 7.088723439 and -7.088723439.Subproblem 1
n + 4.5 = 7.088723439 Simplifying n + 4.5 = 7.088723439 Reorder the terms: 4.5 + n = 7.088723439 Solving 4.5 + n = 7.088723439 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + n = 7.088723439 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + n = 7.088723439 + -4.5 n = 7.088723439 + -4.5 Combine like terms: 7.088723439 + -4.5 = 2.588723439 n = 2.588723439 Simplifying n = 2.588723439Subproblem 2
n + 4.5 = -7.088723439 Simplifying n + 4.5 = -7.088723439 Reorder the terms: 4.5 + n = -7.088723439 Solving 4.5 + n = -7.088723439 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + n = -7.088723439 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + n = -7.088723439 + -4.5 n = -7.088723439 + -4.5 Combine like terms: -7.088723439 + -4.5 = -11.588723439 n = -11.588723439 Simplifying n = -11.588723439Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.588723439, -11.588723439}
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