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Simplifying n2 + 7n + -15 = 5 Reorder the terms: -15 + 7n + n2 = 5 Solving -15 + 7n + n2 = 5 Solving for variable 'n'. Reorder the terms: -15 + -5 + 7n + n2 = 5 + -5 Combine like terms: -15 + -5 = -20 -20 + 7n + n2 = 5 + -5 Combine like terms: 5 + -5 = 0 -20 + 7n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 7n + 20 + n2 = 0 + 20 Reorder the terms: -20 + 20 + 7n + n2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 7n + n2 = 0 + 20 7n + n2 = 0 + 20 Combine like terms: 0 + 20 = 20 7n + n2 = 20 The n term is 7n. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7n + 12.25 + n2 = 20 + 12.25 Reorder the terms: 12.25 + 7n + n2 = 20 + 12.25 Combine like terms: 20 + 12.25 = 32.25 12.25 + 7n + n2 = 32.25 Factor a perfect square on the left side: (n + 3.5)(n + 3.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (n + 3.5) equal to 5.678908346 and -5.678908346.Subproblem 1
n + 3.5 = 5.678908346 Simplifying n + 3.5 = 5.678908346 Reorder the terms: 3.5 + n = 5.678908346 Solving 3.5 + n = 5.678908346 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + n = 5.678908346 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = 5.678908346 + -3.5 n = 5.678908346 + -3.5 Combine like terms: 5.678908346 + -3.5 = 2.178908346 n = 2.178908346 Simplifying n = 2.178908346Subproblem 2
n + 3.5 = -5.678908346 Simplifying n + 3.5 = -5.678908346 Reorder the terms: 3.5 + n = -5.678908346 Solving 3.5 + n = -5.678908346 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + n = -5.678908346 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = -5.678908346 + -3.5 n = -5.678908346 + -3.5 Combine like terms: -5.678908346 + -3.5 = -9.178908346 n = -9.178908346 Simplifying n = -9.178908346Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.178908346, -9.178908346}
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