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Simplifying n2 + 39n + -420 = 0 Reorder the terms: -420 + 39n + n2 = 0 Solving -420 + 39n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '420' to each side of the equation. -420 + 39n + 420 + n2 = 0 + 420 Reorder the terms: -420 + 420 + 39n + n2 = 0 + 420 Combine like terms: -420 + 420 = 0 0 + 39n + n2 = 0 + 420 39n + n2 = 0 + 420 Combine like terms: 0 + 420 = 420 39n + n2 = 420 The n term is 39n. Take half its coefficient (19.5). Square it (380.25) and add it to both sides. Add '380.25' to each side of the equation. 39n + 380.25 + n2 = 420 + 380.25 Reorder the terms: 380.25 + 39n + n2 = 420 + 380.25 Combine like terms: 420 + 380.25 = 800.25 380.25 + 39n + n2 = 800.25 Factor a perfect square on the left side: (n + 19.5)(n + 19.5) = 800.25 Calculate the square root of the right side: 28.28869032 Break this problem into two subproblems by setting (n + 19.5) equal to 28.28869032 and -28.28869032.Subproblem 1
n + 19.5 = 28.28869032 Simplifying n + 19.5 = 28.28869032 Reorder the terms: 19.5 + n = 28.28869032 Solving 19.5 + n = 28.28869032 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-19.5' to each side of the equation. 19.5 + -19.5 + n = 28.28869032 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + n = 28.28869032 + -19.5 n = 28.28869032 + -19.5 Combine like terms: 28.28869032 + -19.5 = 8.78869032 n = 8.78869032 Simplifying n = 8.78869032Subproblem 2
n + 19.5 = -28.28869032 Simplifying n + 19.5 = -28.28869032 Reorder the terms: 19.5 + n = -28.28869032 Solving 19.5 + n = -28.28869032 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-19.5' to each side of the equation. 19.5 + -19.5 + n = -28.28869032 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + n = -28.28869032 + -19.5 n = -28.28869032 + -19.5 Combine like terms: -28.28869032 + -19.5 = -47.78869032 n = -47.78869032 Simplifying n = -47.78869032Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.78869032, -47.78869032}
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