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Simplifying n2 + 20n + 12 = 0 Reorder the terms: 12 + 20n + n2 = 0 Solving 12 + 20n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 20n + -12 + n2 = 0 + -12 Reorder the terms: 12 + -12 + 20n + n2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 20n + n2 = 0 + -12 20n + n2 = 0 + -12 Combine like terms: 0 + -12 = -12 20n + n2 = -12 The n term is 20n. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20n + 100 + n2 = -12 + 100 Reorder the terms: 100 + 20n + n2 = -12 + 100 Combine like terms: -12 + 100 = 88 100 + 20n + n2 = 88 Factor a perfect square on the left side: (n + 10)(n + 10) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (n + 10) equal to 9.38083152 and -9.38083152.Subproblem 1
n + 10 = 9.38083152 Simplifying n + 10 = 9.38083152 Reorder the terms: 10 + n = 9.38083152 Solving 10 + n = 9.38083152 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + n = 9.38083152 + -10 Combine like terms: 10 + -10 = 0 0 + n = 9.38083152 + -10 n = 9.38083152 + -10 Combine like terms: 9.38083152 + -10 = -0.61916848 n = -0.61916848 Simplifying n = -0.61916848Subproblem 2
n + 10 = -9.38083152 Simplifying n + 10 = -9.38083152 Reorder the terms: 10 + n = -9.38083152 Solving 10 + n = -9.38083152 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + n = -9.38083152 + -10 Combine like terms: 10 + -10 = 0 0 + n = -9.38083152 + -10 n = -9.38083152 + -10 Combine like terms: -9.38083152 + -10 = -19.38083152 n = -19.38083152 Simplifying n = -19.38083152Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.61916848, -19.38083152}
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