n^2+10n-40=-8

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Solution for n^2+10n-40=-8 equation:


Simplifying
n2 + 10n + -40 = -8

Reorder the terms:
-40 + 10n + n2 = -8

Solving
-40 + 10n + n2 = -8

Solving for variable 'n'.

Reorder the terms:
-40 + 8 + 10n + n2 = -8 + 8

Combine like terms: -40 + 8 = -32
-32 + 10n + n2 = -8 + 8

Combine like terms: -8 + 8 = 0
-32 + 10n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 10n + 32 + n2 = 0 + 32

Reorder the terms:
-32 + 32 + 10n + n2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 10n + n2 = 0 + 32
10n + n2 = 0 + 32

Combine like terms: 0 + 32 = 32
10n + n2 = 32

The n term is 10n.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10n + 25 + n2 = 32 + 25

Reorder the terms:
25 + 10n + n2 = 32 + 25

Combine like terms: 32 + 25 = 57
25 + 10n + n2 = 57

Factor a perfect square on the left side:
(n + 5)(n + 5) = 57

Calculate the square root of the right side: 7.549834435

Break this problem into two subproblems by setting 
(n + 5) equal to 7.549834435 and -7.549834435.

Subproblem 1

n + 5 = 7.549834435 Simplifying n + 5 = 7.549834435 Reorder the terms: 5 + n = 7.549834435 Solving 5 + n = 7.549834435 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + n = 7.549834435 + -5 Combine like terms: 5 + -5 = 0 0 + n = 7.549834435 + -5 n = 7.549834435 + -5 Combine like terms: 7.549834435 + -5 = 2.549834435 n = 2.549834435 Simplifying n = 2.549834435

Subproblem 2

n + 5 = -7.549834435 Simplifying n + 5 = -7.549834435 Reorder the terms: 5 + n = -7.549834435 Solving 5 + n = -7.549834435 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + n = -7.549834435 + -5 Combine like terms: 5 + -5 = 0 0 + n = -7.549834435 + -5 n = -7.549834435 + -5 Combine like terms: -7.549834435 + -5 = -12.549834435 n = -12.549834435 Simplifying n = -12.549834435

Solution

The solution to the problem is based on the solutions from the subproblems. n = {2.549834435, -12.549834435}

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