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Simplifying n2 + 7n + -9 = 0 Reorder the terms: -9 + 7n + n2 = 0 Solving -9 + 7n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 7n + 9 + n2 = 0 + 9 Reorder the terms: -9 + 9 + 7n + n2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 7n + n2 = 0 + 9 7n + n2 = 0 + 9 Combine like terms: 0 + 9 = 9 7n + n2 = 9 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 = 9 + 12.25 Reorder the terms: 12.25 + 7n + n2 = 9 + 12.25 Combine like terms: 9 + 12.25 = 21.25 12.25 + 7n + n2 = 21.25 Factor a perfect square on the left side: (n + 3.5)(n + 3.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (n + 3.5) equal to 4.609772229 and -4.609772229.Subproblem 1
n + 3.5 = 4.609772229 Simplifying n + 3.5 = 4.609772229 Reorder the terms: 3.5 + n = 4.609772229 Solving 3.5 + n = 4.609772229 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 = 4.609772229 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = 4.609772229 + -3.5 n = 4.609772229 + -3.5 Combine like terms: 4.609772229 + -3.5 = 1.109772229 n = 1.109772229 Simplifying n = 1.109772229Subproblem 2
n + 3.5 = -4.609772229 Simplifying n + 3.5 = -4.609772229 Reorder the terms: 3.5 + n = -4.609772229 Solving 3.5 + n = -4.609772229 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 = -4.609772229 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = -4.609772229 + -3.5 n = -4.609772229 + -3.5 Combine like terms: -4.609772229 + -3.5 = -8.109772229 n = -8.109772229 Simplifying n = -8.109772229Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.109772229, -8.109772229}
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