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Simplifying n2 + -12n + -62 = 0 Reorder the terms: -62 + -12n + n2 = 0 Solving -62 + -12n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '62' to each side of the equation. -62 + -12n + 62 + n2 = 0 + 62 Reorder the terms: -62 + 62 + -12n + n2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + -12n + n2 = 0 + 62 -12n + n2 = 0 + 62 Combine like terms: 0 + 62 = 62 -12n + n2 = 62 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 = 62 + 36 Reorder the terms: 36 + -12n + n2 = 62 + 36 Combine like terms: 62 + 36 = 98 36 + -12n + n2 = 98 Factor a perfect square on the left side: (n + -6)(n + -6) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (n + -6) equal to 9.899494937 and -9.899494937.Subproblem 1
n + -6 = 9.899494937 Simplifying n + -6 = 9.899494937 Reorder the terms: -6 + n = 9.899494937 Solving -6 + n = 9.899494937 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 = 9.899494937 + 6 Combine like terms: -6 + 6 = 0 0 + n = 9.899494937 + 6 n = 9.899494937 + 6 Combine like terms: 9.899494937 + 6 = 15.899494937 n = 15.899494937 Simplifying n = 15.899494937Subproblem 2
n + -6 = -9.899494937 Simplifying n + -6 = -9.899494937 Reorder the terms: -6 + n = -9.899494937 Solving -6 + n = -9.899494937 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 = -9.899494937 + 6 Combine like terms: -6 + 6 = 0 0 + n = -9.899494937 + 6 n = -9.899494937 + 6 Combine like terms: -9.899494937 + 6 = -3.899494937 n = -3.899494937 Simplifying n = -3.899494937Solution
The solution to the problem is based on the solutions from the subproblems. n = {15.899494937, -3.899494937}
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