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Simplifying n2 + -12n + -2 = 0 Reorder the terms: -2 + -12n + n2 = 0 Solving -2 + -12n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -12n + 2 + n2 = 0 + 2 Reorder the terms: -2 + 2 + -12n + n2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -12n + n2 = 0 + 2 -12n + n2 = 0 + 2 Combine like terms: 0 + 2 = 2 -12n + n2 = 2 The n term is -12n. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12n + 36 + n2 = 2 + 36 Reorder the terms: 36 + -12n + n2 = 2 + 36 Combine like terms: 2 + 36 = 38 36 + -12n + n2 = 38 Factor a perfect square on the left side: (n + -6)(n + -6) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (n + -6) equal to 6.164414003 and -6.164414003.Subproblem 1
n + -6 = 6.164414003 Simplifying n + -6 = 6.164414003 Reorder the terms: -6 + n = 6.164414003 Solving -6 + n = 6.164414003 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + n = 6.164414003 + 6 Combine like terms: -6 + 6 = 0 0 + n = 6.164414003 + 6 n = 6.164414003 + 6 Combine like terms: 6.164414003 + 6 = 12.164414003 n = 12.164414003 Simplifying n = 12.164414003Subproblem 2
n + -6 = -6.164414003 Simplifying n + -6 = -6.164414003 Reorder the terms: -6 + n = -6.164414003 Solving -6 + n = -6.164414003 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + n = -6.164414003 + 6 Combine like terms: -6 + 6 = 0 0 + n = -6.164414003 + 6 n = -6.164414003 + 6 Combine like terms: -6.164414003 + 6 = -0.164414003 n = -0.164414003 Simplifying n = -0.164414003Solution
The solution to the problem is based on the solutions from the subproblems. n = {12.164414003, -0.164414003}
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