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Simplifying n2 + 6n + -65 = 0 Reorder the terms: -65 + 6n + n2 = 0 Solving -65 + 6n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '65' to each side of the equation. -65 + 6n + 65 + n2 = 0 + 65 Reorder the terms: -65 + 65 + 6n + n2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + 6n + n2 = 0 + 65 6n + n2 = 0 + 65 Combine like terms: 0 + 65 = 65 6n + n2 = 65 The n term is 6n. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6n + 9 + n2 = 65 + 9 Reorder the terms: 9 + 6n + n2 = 65 + 9 Combine like terms: 65 + 9 = 74 9 + 6n + n2 = 74 Factor a perfect square on the left side: (n + 3)(n + 3) = 74 Calculate the square root of the right side: 8.602325267 Break this problem into two subproblems by setting (n + 3) equal to 8.602325267 and -8.602325267.Subproblem 1
n + 3 = 8.602325267 Simplifying n + 3 = 8.602325267 Reorder the terms: 3 + n = 8.602325267 Solving 3 + n = 8.602325267 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + n = 8.602325267 + -3 Combine like terms: 3 + -3 = 0 0 + n = 8.602325267 + -3 n = 8.602325267 + -3 Combine like terms: 8.602325267 + -3 = 5.602325267 n = 5.602325267 Simplifying n = 5.602325267Subproblem 2
n + 3 = -8.602325267 Simplifying n + 3 = -8.602325267 Reorder the terms: 3 + n = -8.602325267 Solving 3 + n = -8.602325267 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + n = -8.602325267 + -3 Combine like terms: 3 + -3 = 0 0 + n = -8.602325267 + -3 n = -8.602325267 + -3 Combine like terms: -8.602325267 + -3 = -11.602325267 n = -11.602325267 Simplifying n = -11.602325267Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.602325267, -11.602325267}
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