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Simplifying n2 + -24n + -44 = 0 Reorder the terms: -44 + -24n + n2 = 0 Solving -44 + -24n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + -24n + 44 + n2 = 0 + 44 Reorder the terms: -44 + 44 + -24n + n2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + -24n + n2 = 0 + 44 -24n + n2 = 0 + 44 Combine like terms: 0 + 44 = 44 -24n + n2 = 44 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 = 44 + 144 Reorder the terms: 144 + -24n + n2 = 44 + 144 Combine like terms: 44 + 144 = 188 144 + -24n + n2 = 188 Factor a perfect square on the left side: (n + -12)(n + -12) = 188 Calculate the square root of the right side: 13.711309201 Break this problem into two subproblems by setting (n + -12) equal to 13.711309201 and -13.711309201.Subproblem 1
n + -12 = 13.711309201 Simplifying n + -12 = 13.711309201 Reorder the terms: -12 + n = 13.711309201 Solving -12 + n = 13.711309201 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 = 13.711309201 + 12 Combine like terms: -12 + 12 = 0 0 + n = 13.711309201 + 12 n = 13.711309201 + 12 Combine like terms: 13.711309201 + 12 = 25.711309201 n = 25.711309201 Simplifying n = 25.711309201Subproblem 2
n + -12 = -13.711309201 Simplifying n + -12 = -13.711309201 Reorder the terms: -12 + n = -13.711309201 Solving -12 + n = -13.711309201 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 = -13.711309201 + 12 Combine like terms: -12 + 12 = 0 0 + n = -13.711309201 + 12 n = -13.711309201 + 12 Combine like terms: -13.711309201 + 12 = -1.711309201 n = -1.711309201 Simplifying n = -1.711309201Solution
The solution to the problem is based on the solutions from the subproblems. n = {25.711309201, -1.711309201}
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