15v=v^2-14

Simple and best practice solution for 15v=v^2-14 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 15v=v^2-14 equation:


Simplifying
15v = v2 + -14

Reorder the terms:
15v = -14 + v2

Solving
15v = -14 + v2

Solving for variable 'v'.

Reorder the terms:
14 + 15v + -1v2 = -14 + v2 + 14 + -1v2

Reorder the terms:
14 + 15v + -1v2 = -14 + 14 + v2 + -1v2

Combine like terms: -14 + 14 = 0
14 + 15v + -1v2 = 0 + v2 + -1v2
14 + 15v + -1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
14 + 15v + -1v2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-14 + -15v + v2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -15v + 14 + v2 = 0 + 14

Reorder the terms:
-14 + 14 + -15v + v2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -15v + v2 = 0 + 14
-15v + v2 = 0 + 14

Combine like terms: 0 + 14 = 14
-15v + v2 = 14

The v term is -15v.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15v + 56.25 + v2 = 14 + 56.25

Reorder the terms:
56.25 + -15v + v2 = 14 + 56.25

Combine like terms: 14 + 56.25 = 70.25
56.25 + -15v + v2 = 70.25

Factor a perfect square on the left side:
(v + -7.5)(v + -7.5) = 70.25

Calculate the square root of the right side: 8.381527307

Break this problem into two subproblems by setting 
(v + -7.5) equal to 8.381527307 and -8.381527307.

Subproblem 1

v + -7.5 = 8.381527307 Simplifying v + -7.5 = 8.381527307 Reorder the terms: -7.5 + v = 8.381527307 Solving -7.5 + v = 8.381527307 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + v = 8.381527307 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + v = 8.381527307 + 7.5 v = 8.381527307 + 7.5 Combine like terms: 8.381527307 + 7.5 = 15.881527307 v = 15.881527307 Simplifying v = 15.881527307

Subproblem 2

v + -7.5 = -8.381527307 Simplifying v + -7.5 = -8.381527307 Reorder the terms: -7.5 + v = -8.381527307 Solving -7.5 + v = -8.381527307 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + v = -8.381527307 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + v = -8.381527307 + 7.5 v = -8.381527307 + 7.5 Combine like terms: -8.381527307 + 7.5 = -0.881527307 v = -0.881527307 Simplifying v = -0.881527307

Solution

The solution to the problem is based on the solutions from the subproblems. v = {15.881527307, -0.881527307}

See similar equations:

| 4c+3-c=-7+2+c | | 5b-10=7b+12 | | V^2-14=5b | | 5y-x+6=0 | | -8+9b=2+14b | | 5p+2=2p+14 | | 5(c-7)-2(3x-4)=3x | | 2r^2=20r-42 | | 16x+8+10x-10=180 | | 15x+3=-14x+5 | | 3x+6+5x=46 | | 7+3a=-1-5a | | X+5=x-7 | | 14x+6=42 | | -3000x^2+7500=0 | | -2y+5(y-7)=-17 | | X-3i= | | -5m-2=8 | | 10x+15+3x+35=180 | | x-4=12+5x | | 12=9+3x | | X-(6)=-23 | | 96x-1+85x=180 | | 184=3(-7a+8)+a | | 9+-0= | | 106x-1+77x-2=180 | | -62=8(6v+2)-6(v-1) | | 7(u+2)-5u=-2 | | 5(-3)-(-6)= | | 21(x+1)-14(x-1)=21x | | 3(x-24)+3(x-2)=18 | | 2n-6=9+5n |

Equations solver categories