n^2+8n-40=9

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Solution for n^2+8n-40=9 equation:


Simplifying
n2 + 8n + -40 = 9

Reorder the terms:
-40 + 8n + n2 = 9

Solving
-40 + 8n + n2 = 9

Solving for variable 'n'.

Reorder the terms:
-40 + -9 + 8n + n2 = 9 + -9

Combine like terms: -40 + -9 = -49
-49 + 8n + n2 = 9 + -9

Combine like terms: 9 + -9 = 0
-49 + 8n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + 8n + 49 + n2 = 0 + 49

Reorder the terms:
-49 + 49 + 8n + n2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + 8n + n2 = 0 + 49
8n + n2 = 0 + 49

Combine like terms: 0 + 49 = 49
8n + n2 = 49

The n term is 8n.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8n + 16 + n2 = 49 + 16

Reorder the terms:
16 + 8n + n2 = 49 + 16

Combine like terms: 49 + 16 = 65
16 + 8n + n2 = 65

Factor a perfect square on the left side:
(n + 4)(n + 4) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(n + 4) equal to 8.062257748 and -8.062257748.

Subproblem 1

n + 4 = 8.062257748 Simplifying n + 4 = 8.062257748 Reorder the terms: 4 + n = 8.062257748 Solving 4 + n = 8.062257748 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + n = 8.062257748 + -4 Combine like terms: 4 + -4 = 0 0 + n = 8.062257748 + -4 n = 8.062257748 + -4 Combine like terms: 8.062257748 + -4 = 4.062257748 n = 4.062257748 Simplifying n = 4.062257748

Subproblem 2

n + 4 = -8.062257748 Simplifying n + 4 = -8.062257748 Reorder the terms: 4 + n = -8.062257748 Solving 4 + n = -8.062257748 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + n = -8.062257748 + -4 Combine like terms: 4 + -4 = 0 0 + n = -8.062257748 + -4 n = -8.062257748 + -4 Combine like terms: -8.062257748 + -4 = -12.062257748 n = -12.062257748 Simplifying n = -12.062257748

Solution

The solution to the problem is based on the solutions from the subproblems. n = {4.062257748, -12.062257748}

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