v^2+5v+1=0

Simple and best practice solution for v^2+5v+1=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 v^2+5v+1=0 equation: 


Simplifying
v2 + 5v + 1 = 0

Reorder the terms:
1 + 5v + v2 = 0

Solving
1 + 5v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 5v + -1 + v2 = 0 + -1

Reorder the terms:
1 + -1 + 5v + v2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5v + v2 = 0 + -1
5v + v2 = 0 + -1

Combine like terms: 0 + -1 = -1
5v + v2 = -1

The v term is 5v.  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.
5v + 6.25 + v2 = -1 + 6.25

Reorder the terms:
6.25 + 5v + v2 = -1 + 6.25

Combine like terms: -1 + 6.25 = 5.25
6.25 + 5v + v2 = 5.25

Factor a perfect square on the left side:
(v + 2.5)(v + 2.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(v + 2.5) equal to 2.291287847 and -2.291287847.


Subproblem 1
v + 2.5 = 2.291287847

Simplifying
v + 2.5 = 2.291287847

Reorder the terms:
2.5 + v = 2.291287847

Solving
2.5 + v = 2.291287847

Solving for variable 'v'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + v = 2.291287847 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + v = 2.291287847 + -2.5
v = 2.291287847 + -2.5

Combine like terms: 2.291287847 + -2.5 = -0.208712153
v = -0.208712153

Simplifying
v = -0.208712153


Subproblem 2
v + 2.5 = -2.291287847

Simplifying
v + 2.5 = -2.291287847

Reorder the terms:
2.5 + v = -2.291287847

Solving
2.5 + v = -2.291287847

Solving for variable 'v'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + v = -2.291287847 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + v = -2.291287847 + -2.5
v = -2.291287847 + -2.5

Combine like terms: -2.291287847 + -2.5 = -4.791287847
v = -4.791287847

Simplifying
v = -4.791287847


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-0.208712153, -4.791287847}

See similar equations:

| 2w*4w= | | 20000*x=5000*4x | | (nk-9)3=5k | | nk-9/3=5k | | 6s^2-s-2=0 | | xk-9k=10 | | 3m+10=28# | | 7(45+6)=322 | | 7(2l+6)=140 | | (q-5)*4=24 | | (1-x)(-1-x)+.75=0 | | 5+4*a=b | | (12×4/x^(4/7))-(3×4/x^(4/7))=x^(10/7) | | 9/8*-18.6 | | 1-y=19.6 | | y=2.52x+1.61 | | y^2-3y-3/2 | | 1/2xy-200y=20000 | | x+(x*.1)=131 | | x+(x*.1)=286 | | .30(x)+.13(x+50)=.20(x+50) | | -2.5x+5+3x=-12 | | 2.5x+5+3x=12 | | 142=6x+2 | | 3[10+(3n-1)-(4-n)]=5(n+10) | | 13+6x-7x= | | 6x-4+4-7x= | | 8+2(x+5)+3(x+5)= | | -3(-7v+5)-9v=2(v-2)-3 | | 9xh-17=5xh+3 | | xln(x)=20 | | 2x+11=6x+25 |

Equations solver categories