n^2+11n-4=0

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Solution for n^2+11n-4=0 equation:


Simplifying
n2 + 11n + -4 = 0

Reorder the terms:
-4 + 11n + n2 = 0

Solving
-4 + 11n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 11n + 4 + n2 = 0 + 4

Reorder the terms:
-4 + 4 + 11n + n2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 11n + n2 = 0 + 4
11n + n2 = 0 + 4

Combine like terms: 0 + 4 = 4
11n + n2 = 4

The n term is 11n.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11n + 30.25 + n2 = 4 + 30.25

Reorder the terms:
30.25 + 11n + n2 = 4 + 30.25

Combine like terms: 4 + 30.25 = 34.25
30.25 + 11n + n2 = 34.25

Factor a perfect square on the left side:
(n + 5.5)(n + 5.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(n + 5.5) equal to 5.852349955 and -5.852349955.

Subproblem 1

n + 5.5 = 5.852349955 Simplifying n + 5.5 = 5.852349955 Reorder the terms: 5.5 + n = 5.852349955 Solving 5.5 + n = 5.852349955 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + n = 5.852349955 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + n = 5.852349955 + -5.5 n = 5.852349955 + -5.5 Combine like terms: 5.852349955 + -5.5 = 0.352349955 n = 0.352349955 Simplifying n = 0.352349955

Subproblem 2

n + 5.5 = -5.852349955 Simplifying n + 5.5 = -5.852349955 Reorder the terms: 5.5 + n = -5.852349955 Solving 5.5 + n = -5.852349955 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + n = -5.852349955 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + n = -5.852349955 + -5.5 n = -5.852349955 + -5.5 Combine like terms: -5.852349955 + -5.5 = -11.352349955 n = -11.352349955 Simplifying n = -11.352349955

Solution

The solution to the problem is based on the solutions from the subproblems. n = {0.352349955, -11.352349955}

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