v^2+10v-19=0

Simple and best practice solution for v^2+10v-19=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+10v-19=0 equation:


Simplifying
v2 + 10v + -19 = 0

Reorder the terms:
-19 + 10v + v2 = 0

Solving
-19 + 10v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + 10v + 19 + v2 = 0 + 19

Reorder the terms:
-19 + 19 + 10v + v2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 10v + v2 = 0 + 19
10v + v2 = 0 + 19

Combine like terms: 0 + 19 = 19
10v + v2 = 19

The v term is 10v.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10v + 25 + v2 = 19 + 25

Reorder the terms:
25 + 10v + v2 = 19 + 25

Combine like terms: 19 + 25 = 44
25 + 10v + v2 = 44

Factor a perfect square on the left side:
(v + 5)(v + 5) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(v + 5) equal to 6.633249581 and -6.633249581.


Subproblem 1
v + 5 = 6.633249581

Simplifying
v + 5 = 6.633249581

Reorder the terms:
5 + v = 6.633249581

Solving
5 + v = 6.633249581

Solving for variable 'v'.

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

Add '-5' to each side of the equation.
5 + -5 + v = 6.633249581 + -5

Combine like terms: 5 + -5 = 0
0 + v = 6.633249581 + -5
v = 6.633249581 + -5

Combine like terms: 6.633249581 + -5 = 1.633249581
v = 1.633249581

Simplifying
v = 1.633249581


Subproblem 2
v + 5 = -6.633249581

Simplifying
v + 5 = -6.633249581

Reorder the terms:
5 + v = -6.633249581

Solving
5 + v = -6.633249581

Solving for variable 'v'.

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

Add '-5' to each side of the equation.
5 + -5 + v = -6.633249581 + -5

Combine like terms: 5 + -5 = 0
0 + v = -6.633249581 + -5
v = -6.633249581 + -5

Combine like terms: -6.633249581 + -5 = -11.633249581
v = -11.633249581

Simplifying
v = -11.633249581


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {1.633249581, -11.633249581}

See similar equations:

| 3.2(2x+5)=86.4 | | 37-6x=5-10x | | 45s=5+5s | | 2x=68x | | 0=(x+3)(x+3) | | 6+2(3x-2)=14-2x | | 11x-5=6x+6 | | 15x^2-44x-36=0 | | 2x+4=-10+4x | | 1-4t-t=0 | | 12-7a=-31 | | 56x^4-8x^3= | | 8x^2+32=32x | | (3x+10)=10 | | 4y+2y=18 | | 4x+10=-35-5x | | x+12y=-7 | | 12k+8= | | 9h-8=-6h+7 | | 9m+6=96 | | (a-5)(4a+1)=0 | | (2x+3)(2x+3)-36=0 | | 3(4x+6)-2=12x+16 | | y^5-0.5y^4+y^3+y-0.25=0 | | 2x-3y-z=1 | | -3(3+2g)=9 | | 97+x+27+64+97+x=180 | | 3+4n-9+2=30 | | z^2-10=-41 | | y^8-4y^5+2y^4-4y^3-4y+1=0 | | -x+y-3z=5 | | 6x-1=10x+4 |

Equations solver categories