5v^2-26v=19

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Solution for 5v^2-26v=19 equation:


Simplifying
5v2 + -26v = 19

Reorder the terms:
-26v + 5v2 = 19

Solving
-26v + 5v2 = 19

Solving for variable 'v'.

Reorder the terms:
-19 + -26v + 5v2 = 19 + -19

Combine like terms: 19 + -19 = 0
-19 + -26v + 5v2 = 0

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

Divide each side by '5'.
-3.8 + -5.2v + v2 = 0

Move the constant term to the right:

Add '3.8' to each side of the equation.
-3.8 + -5.2v + 3.8 + v2 = 0 + 3.8

Reorder the terms:
-3.8 + 3.8 + -5.2v + v2 = 0 + 3.8

Combine like terms: -3.8 + 3.8 = 0.0
0.0 + -5.2v + v2 = 0 + 3.8
-5.2v + v2 = 0 + 3.8

Combine like terms: 0 + 3.8 = 3.8
-5.2v + v2 = 3.8

The v term is -5.2v.  Take half its coefficient (-2.6).
Square it (6.76) and add it to both sides.

Add '6.76' to each side of the equation.
-5.2v + 6.76 + v2 = 3.8 + 6.76

Reorder the terms:
6.76 + -5.2v + v2 = 3.8 + 6.76

Combine like terms: 3.8 + 6.76 = 10.56
6.76 + -5.2v + v2 = 10.56

Factor a perfect square on the left side:
(v + -2.6)(v + -2.6) = 10.56

Calculate the square root of the right side: 3.249615362

Break this problem into two subproblems by setting 
(v + -2.6) equal to 3.249615362 and -3.249615362.

Subproblem 1

v + -2.6 = 3.249615362 Simplifying v + -2.6 = 3.249615362 Reorder the terms: -2.6 + v = 3.249615362 Solving -2.6 + v = 3.249615362 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + v = 3.249615362 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + v = 3.249615362 + 2.6 v = 3.249615362 + 2.6 Combine like terms: 3.249615362 + 2.6 = 5.849615362 v = 5.849615362 Simplifying v = 5.849615362

Subproblem 2

v + -2.6 = -3.249615362 Simplifying v + -2.6 = -3.249615362 Reorder the terms: -2.6 + v = -3.249615362 Solving -2.6 + v = -3.249615362 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + v = -3.249615362 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + v = -3.249615362 + 2.6 v = -3.249615362 + 2.6 Combine like terms: -3.249615362 + 2.6 = -0.649615362 v = -0.649615362 Simplifying v = -0.649615362

Solution

The solution to the problem is based on the solutions from the subproblems. v = {5.849615362, -0.649615362}

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