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Simplifying n2 + -3n + -36 = 0 Reorder the terms: -36 + -3n + n2 = 0 Solving -36 + -3n + 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 + -3n + 36 + n2 = 0 + 36 Reorder the terms: -36 + 36 + -3n + n2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -3n + n2 = 0 + 36 -3n + n2 = 0 + 36 Combine like terms: 0 + 36 = 36 -3n + n2 = 36 The n term is -3n. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3n + 2.25 + n2 = 36 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 36 + 2.25 Combine like terms: 36 + 2.25 = 38.25 2.25 + -3n + n2 = 38.25 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (n + -1.5) equal to 6.184658438 and -6.184658438.Subproblem 1
n + -1.5 = 6.184658438 Simplifying n + -1.5 = 6.184658438 Reorder the terms: -1.5 + n = 6.184658438 Solving -1.5 + n = 6.184658438 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 6.184658438 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 6.184658438 + 1.5 n = 6.184658438 + 1.5 Combine like terms: 6.184658438 + 1.5 = 7.684658438 n = 7.684658438 Simplifying n = 7.684658438Subproblem 2
n + -1.5 = -6.184658438 Simplifying n + -1.5 = -6.184658438 Reorder the terms: -1.5 + n = -6.184658438 Solving -1.5 + n = -6.184658438 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -6.184658438 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -6.184658438 + 1.5 n = -6.184658438 + 1.5 Combine like terms: -6.184658438 + 1.5 = -4.684658438 n = -4.684658438 Simplifying n = -4.684658438Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.684658438, -4.684658438}
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