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Simplifying n2 + -24n + -36 = 0 Reorder the terms: -36 + -24n + n2 = 0 Solving -36 + -24n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -24n + 36 + n2 = 0 + 36 Reorder the terms: -36 + 36 + -24n + n2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -24n + n2 = 0 + 36 -24n + n2 = 0 + 36 Combine like terms: 0 + 36 = 36 -24n + n2 = 36 The n term is -24n. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24n + 144 + n2 = 36 + 144 Reorder the terms: 144 + -24n + n2 = 36 + 144 Combine like terms: 36 + 144 = 180 144 + -24n + n2 = 180 Factor a perfect square on the left side: (n + -12)(n + -12) = 180 Calculate the square root of the right side: 13.416407865 Break this problem into two subproblems by setting (n + -12) equal to 13.416407865 and -13.416407865.Subproblem 1
n + -12 = 13.416407865 Simplifying n + -12 = 13.416407865 Reorder the terms: -12 + n = 13.416407865 Solving -12 + n = 13.416407865 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + n = 13.416407865 + 12 Combine like terms: -12 + 12 = 0 0 + n = 13.416407865 + 12 n = 13.416407865 + 12 Combine like terms: 13.416407865 + 12 = 25.416407865 n = 25.416407865 Simplifying n = 25.416407865Subproblem 2
n + -12 = -13.416407865 Simplifying n + -12 = -13.416407865 Reorder the terms: -12 + n = -13.416407865 Solving -12 + n = -13.416407865 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + n = -13.416407865 + 12 Combine like terms: -12 + 12 = 0 0 + n = -13.416407865 + 12 n = -13.416407865 + 12 Combine like terms: -13.416407865 + 12 = -1.416407865 n = -1.416407865 Simplifying n = -1.416407865Solution
The solution to the problem is based on the solutions from the subproblems. n = {25.416407865, -1.416407865}
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