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Simplifying n2 + -1n + -38 = 0 Reorder the terms: -38 + -1n + n2 = 0 Solving -38 + -1n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + -1n + 38 + n2 = 0 + 38 Reorder the terms: -38 + 38 + -1n + n2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + -1n + n2 = 0 + 38 -1n + n2 = 0 + 38 Combine like terms: 0 + 38 = 38 -1n + n2 = 38 The n term is -1n. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = 38 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 38 + 0.25 Combine like terms: 38 + 0.25 = 38.25 0.25 + -1n + n2 = 38.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (n + -0.5) equal to 6.184658438 and -6.184658438.Subproblem 1
n + -0.5 = 6.184658438 Simplifying n + -0.5 = 6.184658438 Reorder the terms: -0.5 + n = 6.184658438 Solving -0.5 + n = 6.184658438 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = 6.184658438 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 6.184658438 + 0.5 n = 6.184658438 + 0.5 Combine like terms: 6.184658438 + 0.5 = 6.684658438 n = 6.684658438 Simplifying n = 6.684658438Subproblem 2
n + -0.5 = -6.184658438 Simplifying n + -0.5 = -6.184658438 Reorder the terms: -0.5 + n = -6.184658438 Solving -0.5 + n = -6.184658438 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = -6.184658438 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -6.184658438 + 0.5 n = -6.184658438 + 0.5 Combine like terms: -6.184658438 + 0.5 = -5.684658438 n = -5.684658438 Simplifying n = -5.684658438Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.684658438, -5.684658438}
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