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Simplifying n2 + 9n + -300 = 0 Reorder the terms: -300 + 9n + n2 = 0 Solving -300 + 9n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '300' to each side of the equation. -300 + 9n + 300 + n2 = 0 + 300 Reorder the terms: -300 + 300 + 9n + n2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 9n + n2 = 0 + 300 9n + n2 = 0 + 300 Combine like terms: 0 + 300 = 300 9n + n2 = 300 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 = 300 + 20.25 Reorder the terms: 20.25 + 9n + n2 = 300 + 20.25 Combine like terms: 300 + 20.25 = 320.25 20.25 + 9n + n2 = 320.25 Factor a perfect square on the left side: (n + 4.5)(n + 4.5) = 320.25 Calculate the square root of the right side: 17.895530168 Break this problem into two subproblems by setting (n + 4.5) equal to 17.895530168 and -17.895530168.Subproblem 1
n + 4.5 = 17.895530168 Simplifying n + 4.5 = 17.895530168 Reorder the terms: 4.5 + n = 17.895530168 Solving 4.5 + n = 17.895530168 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 = 17.895530168 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + n = 17.895530168 + -4.5 n = 17.895530168 + -4.5 Combine like terms: 17.895530168 + -4.5 = 13.395530168 n = 13.395530168 Simplifying n = 13.395530168Subproblem 2
n + 4.5 = -17.895530168 Simplifying n + 4.5 = -17.895530168 Reorder the terms: 4.5 + n = -17.895530168 Solving 4.5 + n = -17.895530168 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 = -17.895530168 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + n = -17.895530168 + -4.5 n = -17.895530168 + -4.5 Combine like terms: -17.895530168 + -4.5 = -22.395530168 n = -22.395530168 Simplifying n = -22.395530168Solution
The solution to the problem is based on the solutions from the subproblems. n = {13.395530168, -22.395530168}
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