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Simplifying 6n + n2 = 144 Solving 6n + n2 = 144 Solving for variable 'n'. Reorder the terms: -144 + 6n + n2 = 144 + -144 Combine like terms: 144 + -144 = 0 -144 + 6n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + 6n + 144 + n2 = 0 + 144 Reorder the terms: -144 + 144 + 6n + n2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 6n + n2 = 0 + 144 6n + n2 = 0 + 144 Combine like terms: 0 + 144 = 144 6n + n2 = 144 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 = 144 + 9 Reorder the terms: 9 + 6n + n2 = 144 + 9 Combine like terms: 144 + 9 = 153 9 + 6n + n2 = 153 Factor a perfect square on the left side: (n + 3)(n + 3) = 153 Calculate the square root of the right side: 12.369316877 Break this problem into two subproblems by setting (n + 3) equal to 12.369316877 and -12.369316877.Subproblem 1
n + 3 = 12.369316877 Simplifying n + 3 = 12.369316877 Reorder the terms: 3 + n = 12.369316877 Solving 3 + n = 12.369316877 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 = 12.369316877 + -3 Combine like terms: 3 + -3 = 0 0 + n = 12.369316877 + -3 n = 12.369316877 + -3 Combine like terms: 12.369316877 + -3 = 9.369316877 n = 9.369316877 Simplifying n = 9.369316877Subproblem 2
n + 3 = -12.369316877 Simplifying n + 3 = -12.369316877 Reorder the terms: 3 + n = -12.369316877 Solving 3 + n = -12.369316877 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 = -12.369316877 + -3 Combine like terms: 3 + -3 = 0 0 + n = -12.369316877 + -3 n = -12.369316877 + -3 Combine like terms: -12.369316877 + -3 = -15.369316877 n = -15.369316877 Simplifying n = -15.369316877Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.369316877, -15.369316877}
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