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Simplifying n2 + -20n + 61 = 4 Reorder the terms: 61 + -20n + n2 = 4 Solving 61 + -20n + n2 = 4 Solving for variable 'n'. Reorder the terms: 61 + -4 + -20n + n2 = 4 + -4 Combine like terms: 61 + -4 = 57 57 + -20n + n2 = 4 + -4 Combine like terms: 4 + -4 = 0 57 + -20n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-57' to each side of the equation. 57 + -20n + -57 + n2 = 0 + -57 Reorder the terms: 57 + -57 + -20n + n2 = 0 + -57 Combine like terms: 57 + -57 = 0 0 + -20n + n2 = 0 + -57 -20n + n2 = 0 + -57 Combine like terms: 0 + -57 = -57 -20n + n2 = -57 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 = -57 + 100 Reorder the terms: 100 + -20n + n2 = -57 + 100 Combine like terms: -57 + 100 = 43 100 + -20n + n2 = 43 Factor a perfect square on the left side: (n + -10)(n + -10) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (n + -10) equal to 6.557438524 and -6.557438524.Subproblem 1
n + -10 = 6.557438524 Simplifying n + -10 = 6.557438524 Reorder the terms: -10 + n = 6.557438524 Solving -10 + n = 6.557438524 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 = 6.557438524 + 10 Combine like terms: -10 + 10 = 0 0 + n = 6.557438524 + 10 n = 6.557438524 + 10 Combine like terms: 6.557438524 + 10 = 16.557438524 n = 16.557438524 Simplifying n = 16.557438524Subproblem 2
n + -10 = -6.557438524 Simplifying n + -10 = -6.557438524 Reorder the terms: -10 + n = -6.557438524 Solving -10 + n = -6.557438524 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 = -6.557438524 + 10 Combine like terms: -10 + 10 = 0 0 + n = -6.557438524 + 10 n = -6.557438524 + 10 Combine like terms: -6.557438524 + 10 = 3.442561476 n = 3.442561476 Simplifying n = 3.442561476Solution
The solution to the problem is based on the solutions from the subproblems. n = {16.557438524, 3.442561476}
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