n^2+5n+2=0

Simple and best practice solution for n^2+5n+2=0 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+5n+2=0 equation: 


Simplifying
n2 + 5n + 2 = 0

Reorder the terms:
2 + 5n + n2 = 0

Solving
2 + 5n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 5n + -2 + n2 = 0 + -2

Reorder the terms:
2 + -2 + 5n + n2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5n + n2 = 0 + -2
5n + n2 = 0 + -2

Combine like terms: 0 + -2 = -2
5n + n2 = -2

The n term is 5n.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5n + 6.25 + n2 = -2 + 6.25

Reorder the terms:
6.25 + 5n + n2 = -2 + 6.25

Combine like terms: -2 + 6.25 = 4.25
6.25 + 5n + n2 = 4.25

Factor a perfect square on the left side:
(n + 2.5)(n + 2.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(n + 2.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
n + 2.5 = 2.061552813

Simplifying
n + 2.5 = 2.061552813

Reorder the terms:
2.5 + n = 2.061552813

Solving
2.5 + n = 2.061552813

Solving for variable 'n'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + n = 2.061552813 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + n = 2.061552813 + -2.5
n = 2.061552813 + -2.5

Combine like terms: 2.061552813 + -2.5 = -0.438447187
n = -0.438447187

Simplifying
n = -0.438447187


Subproblem 2
n + 2.5 = -2.061552813

Simplifying
n + 2.5 = -2.061552813

Reorder the terms:
2.5 + n = -2.061552813

Solving
2.5 + n = -2.061552813

Solving for variable 'n'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + n = -2.061552813 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + n = -2.061552813 + -2.5
n = -2.061552813 + -2.5

Combine like terms: -2.061552813 + -2.5 = -4.561552813
n = -4.561552813

Simplifying
n = -4.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.438447187, -4.561552813}

See similar equations:

| -7(5x-8)+7=-35x+63 | | -14(x-6)=80 | | 2(2a-7)=8 | | -2x+14=-56 | | -6(x+5)=-36 | | 13.19-8.54x=7.94x-1.82 | | 2x+10=80-5 | | 18x-3v/3 | | 35x^2+59x+14=0 | | 11-14x+3x^2=0 | | 8x+18-7x=-2-12 | | 4-4=14x+9x | | 3x^2-14+11=0 | | 5(3x+2)=15x+10 | | 23(x+3)=-640-50 | | 0.04(y-1)+0.20y=0.06y-0.4 | | 0.4(4x+8)=1.5-(x+2) | | -7-5=5x+10-4x | | 5x+5-4x=12 | | 8w-19w=44 | | x-8=-4+6 | | 4(5z+2)=68 | | 2z-9=-52(2z+8) | | -3(x-11)=-36 | | 4b=8 | | 6y+5x=10 | | 6(2a+3)=42 | | 0.50x+0.45(70)=37.5 | | (x)+(x/4)=60 | | 0.043*(-1.6)= | | 5235f-455f=12 | | 16b^2-56b+49= |

Equations solver categories