n^2-4n+1=5

Simple and best practice solution for n^2-4n+1=5 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for n^2-4n+1=5 equation: 


Simplifying
n2 + -4n + 1 = 5

Reorder the terms:
1 + -4n + n2 = 5

Solving
1 + -4n + n2 = 5

Solving for variable 'n'.

Reorder the terms:
1 + -5 + -4n + n2 = 5 + -5

Combine like terms: 1 + -5 = -4
-4 + -4n + n2 = 5 + -5

Combine like terms: 5 + -5 = 0
-4 + -4n + n2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 4 + 4

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

Combine like terms: 4 + 4 = 8
4 + -4n + n2 = 8

Factor a perfect square on the left side:
(n + -2)(n + -2) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(n + -2) equal to 2.828427125 and -2.828427125.


Subproblem 1
n + -2 = 2.828427125

Simplifying
n + -2 = 2.828427125

Reorder the terms:
-2 + n = 2.828427125

Solving
-2 + n = 2.828427125

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 = 2.828427125 + 2

Combine like terms: -2 + 2 = 0
0 + n = 2.828427125 + 2
n = 2.828427125 + 2

Combine like terms: 2.828427125 + 2 = 4.828427125
n = 4.828427125

Simplifying
n = 4.828427125


Subproblem 2
n + -2 = -2.828427125

Simplifying
n + -2 = -2.828427125

Reorder the terms:
-2 + n = -2.828427125

Solving
-2 + n = -2.828427125

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 = -2.828427125 + 2

Combine like terms: -2 + 2 = 0
0 + n = -2.828427125 + 2
n = -2.828427125 + 2

Combine like terms: -2.828427125 + 2 = -0.828427125
n = -0.828427125

Simplifying
n = -0.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {4.828427125, -0.828427125}

See similar equations:

| 5(d-2)+d=13*2d | | 0.5x+70=90 | | 3x+11=-3 | | 4.3(5.6+c)= | | 5x+64=44 | | 2x+39=15 | | 4.2r+8.1s+1.09r+6.32s= | | 6x-85=-37 | | 4x+86=58 | | 2x+10=-52 | | h=-4.9t^2+1.5t+17 | | 18+27m-29+36m= | | 7=-x-10 | | 8(j+12)+4(k-19)= | | 6x+7=-35 | | 9.8c+8d-4.6c+2.9d= | | 8=53-9y | | 5+3(x+7)+10=42 | | x+x*0.35=100 | | s^2-7s+16=0 | | (x+72)(x-8)=0 | | 3x-36=-33 | | 7-4(x+8)+9=35 | | x^2+2x-10=20 | | x^2+y^2=2.25 | | 7.9y+8.4-2.04y= | | 3.09(j+4.6)= | | x+13=y | | 1E-15= | | 6(n-1)+2(n+1)=10+7n | | 4+3(x-7)+8=25 | | 1E-14= |

Equations solver categories