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Simplifying n2 + -24n + 52 = 0 Reorder the terms: 52 + -24n + n2 = 0 Solving 52 + -24n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-52' to each side of the equation. 52 + -24n + -52 + n2 = 0 + -52 Reorder the terms: 52 + -52 + -24n + n2 = 0 + -52 Combine like terms: 52 + -52 = 0 0 + -24n + n2 = 0 + -52 -24n + n2 = 0 + -52 Combine like terms: 0 + -52 = -52 -24n + n2 = -52 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 = -52 + 144 Reorder the terms: 144 + -24n + n2 = -52 + 144 Combine like terms: -52 + 144 = 92 144 + -24n + n2 = 92 Factor a perfect square on the left side: (n + -12)(n + -12) = 92 Calculate the square root of the right side: 9.591663047 Break this problem into two subproblems by setting (n + -12) equal to 9.591663047 and -9.591663047.Subproblem 1
n + -12 = 9.591663047 Simplifying n + -12 = 9.591663047 Reorder the terms: -12 + n = 9.591663047 Solving -12 + n = 9.591663047 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 = 9.591663047 + 12 Combine like terms: -12 + 12 = 0 0 + n = 9.591663047 + 12 n = 9.591663047 + 12 Combine like terms: 9.591663047 + 12 = 21.591663047 n = 21.591663047 Simplifying n = 21.591663047Subproblem 2
n + -12 = -9.591663047 Simplifying n + -12 = -9.591663047 Reorder the terms: -12 + n = -9.591663047 Solving -12 + n = -9.591663047 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 = -9.591663047 + 12 Combine like terms: -12 + 12 = 0 0 + n = -9.591663047 + 12 n = -9.591663047 + 12 Combine like terms: -9.591663047 + 12 = 2.408336953 n = 2.408336953 Simplifying n = 2.408336953Solution
The solution to the problem is based on the solutions from the subproblems. n = {21.591663047, 2.408336953}
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