n^2+n-1=

Simple and best practice solution for n^2+n-1= 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+n-1= equation:


Simplifying
n2 + n + -1 = 0

Reorder the terms:
-1 + n + n2 = 0

Solving
-1 + n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + n + 1 + n2 = 0 + 1

Reorder the terms:
-1 + 1 + n + n2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + n + n2 = 0 + 1
n + n2 = 0 + 1

Combine like terms: 0 + 1 = 1
n + n2 = 1

The n term is n.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
n + 0.25 + n2 = 1 + 0.25

Reorder the terms:
0.25 + n + n2 = 1 + 0.25

Combine like terms: 1 + 0.25 = 1.25
0.25 + n + n2 = 1.25

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(n + 0.5) equal to 1.118033989 and -1.118033989.


Subproblem 1
n + 0.5 = 1.118033989

Simplifying
n + 0.5 = 1.118033989

Reorder the terms:
0.5 + n = 1.118033989

Solving
0.5 + n = 1.118033989

Solving for variable 'n'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + n = 1.118033989 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = 1.118033989 + -0.5
n = 1.118033989 + -0.5

Combine like terms: 1.118033989 + -0.5 = 0.618033989
n = 0.618033989

Simplifying
n = 0.618033989


Subproblem 2
n + 0.5 = -1.118033989

Simplifying
n + 0.5 = -1.118033989

Reorder the terms:
0.5 + n = -1.118033989

Solving
0.5 + n = -1.118033989

Solving for variable 'n'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + n = -1.118033989 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = -1.118033989 + -0.5
n = -1.118033989 + -0.5

Combine like terms: -1.118033989 + -0.5 = -1.618033989
n = -1.618033989

Simplifying
n = -1.618033989


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.618033989, -1.618033989}

See similar equations:

| 12=(x-2)+7 | | n+n-1= | | 70=112+89x-16x^2 | | 2+5x=3x+46 | | 2n+n+1= | | x^3-3/2x^2-36x | | 12=x/-2+7 | | 1/6=x/1.4 | | -2=1(-1n+8) | | -2=1x(-1n+8) | | 15/35=a/175 | | -9=-2-3r | | -2x+10-3x=-45 | | -3(4x-8y)=-3(8) | | 5/x+5=4/x | | -2=1+(-1n+8) | | 5/x+5 | | -3x+0=-4 | | x*4=60 | | -3x+4(2)=-4 | | 3r+22=29 | | -2=1+(1n+8) | | 6+3x=5x+7 | | -3/-12 | | 3(2n-3)=2n+3 | | 4/9=r/6 | | x+19/19=0 | | 5(n-5)+6n=52 | | 3r+22=20 | | -3x+4(0)=-4 | | 40=-5/3y | | -3(0)+4y=-4 |

Equations solver categories