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Simplifying n2 + -6n + -52 = 0 Reorder the terms: -52 + -6n + n2 = 0 Solving -52 + -6n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + -6n + 52 + n2 = 0 + 52 Reorder the terms: -52 + 52 + -6n + n2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -6n + n2 = 0 + 52 -6n + n2 = 0 + 52 Combine like terms: 0 + 52 = 52 -6n + n2 = 52 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 = 52 + 9 Reorder the terms: 9 + -6n + n2 = 52 + 9 Combine like terms: 52 + 9 = 61 9 + -6n + n2 = 61 Factor a perfect square on the left side: (n + -3)(n + -3) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (n + -3) equal to 7.810249676 and -7.810249676.Subproblem 1
n + -3 = 7.810249676 Simplifying n + -3 = 7.810249676 Reorder the terms: -3 + n = 7.810249676 Solving -3 + n = 7.810249676 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 = 7.810249676 + 3 Combine like terms: -3 + 3 = 0 0 + n = 7.810249676 + 3 n = 7.810249676 + 3 Combine like terms: 7.810249676 + 3 = 10.810249676 n = 10.810249676 Simplifying n = 10.810249676Subproblem 2
n + -3 = -7.810249676 Simplifying n + -3 = -7.810249676 Reorder the terms: -3 + n = -7.810249676 Solving -3 + n = -7.810249676 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 = -7.810249676 + 3 Combine like terms: -3 + 3 = 0 0 + n = -7.810249676 + 3 n = -7.810249676 + 3 Combine like terms: -7.810249676 + 3 = -4.810249676 n = -4.810249676 Simplifying n = -4.810249676Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.810249676, -4.810249676}
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