n^2-4n-3=0

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Solution for n^2-4n-3=0 equation: 


Simplifying
n2 + -4n + -3 = 0

Reorder the terms:
-3 + -4n + n2 = 0

Solving
-3 + -4n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -4n + 3 + n2 = 0 + 3

Reorder the terms:
-3 + 3 + -4n + n2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4n + n2 = 0 + 3
-4n + n2 = 0 + 3

Combine like terms: 0 + 3 = 3
-4n + n2 = 3

The n term is -4n.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4n + 4 + n2 = 3 + 4

Reorder the terms:
4 + -4n + n2 = 3 + 4

Combine like terms: 3 + 4 = 7
4 + -4n + n2 = 7

Factor a perfect square on the left side:
(n + -2)(n + -2) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(n + -2) equal to 2.645751311 and -2.645751311.


Subproblem 1
n + -2 = 2.645751311

Simplifying
n + -2 = 2.645751311

Reorder the terms:
-2 + n = 2.645751311

Solving
-2 + n = 2.645751311

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + n = 2.645751311 + 2

Combine like terms: -2 + 2 = 0
0 + n = 2.645751311 + 2
n = 2.645751311 + 2

Combine like terms: 2.645751311 + 2 = 4.645751311
n = 4.645751311

Simplifying
n = 4.645751311


Subproblem 2
n + -2 = -2.645751311

Simplifying
n + -2 = -2.645751311

Reorder the terms:
-2 + n = -2.645751311

Solving
-2 + n = -2.645751311

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + n = -2.645751311 + 2

Combine like terms: -2 + 2 = 0
0 + n = -2.645751311 + 2
n = -2.645751311 + 2

Combine like terms: -2.645751311 + 2 = -0.645751311
n = -0.645751311

Simplifying
n = -0.645751311


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {4.645751311, -0.645751311}

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