-5v^2-8v+6=0

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Solution for -5v^2-8v+6=0 equation:


Simplifying
-5v2 + -8v + 6 = 0

Reorder the terms:
6 + -8v + -5v2 = 0

Solving
6 + -8v + -5v2 = 0

Solving for variable 'v'.

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

Divide each side by '-5'.
-1.2 + 1.6v + v2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + 1.6v + 1.2 + v2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + 1.6v + v2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + 1.6v + v2 = 0 + 1.2
1.6v + v2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
1.6v + v2 = 1.2

The v term is 1.6v.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6v + 0.64 + v2 = 1.2 + 0.64

Reorder the terms:
0.64 + 1.6v + v2 = 1.2 + 0.64

Combine like terms: 1.2 + 0.64 = 1.84
0.64 + 1.6v + v2 = 1.84

Factor a perfect square on the left side:
(v + 0.8)(v + 0.8) = 1.84

Calculate the square root of the right side: 1.356465997

Break this problem into two subproblems by setting 
(v + 0.8) equal to 1.356465997 and -1.356465997.

Subproblem 1

v + 0.8 = 1.356465997 Simplifying v + 0.8 = 1.356465997 Reorder the terms: 0.8 + v = 1.356465997 Solving 0.8 + v = 1.356465997 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + v = 1.356465997 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + v = 1.356465997 + -0.8 v = 1.356465997 + -0.8 Combine like terms: 1.356465997 + -0.8 = 0.556465997 v = 0.556465997 Simplifying v = 0.556465997

Subproblem 2

v + 0.8 = -1.356465997 Simplifying v + 0.8 = -1.356465997 Reorder the terms: 0.8 + v = -1.356465997 Solving 0.8 + v = -1.356465997 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + v = -1.356465997 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + v = -1.356465997 + -0.8 v = -1.356465997 + -0.8 Combine like terms: -1.356465997 + -0.8 = -2.156465997 v = -2.156465997 Simplifying v = -2.156465997

Solution

The solution to the problem is based on the solutions from the subproblems. v = {0.556465997, -2.156465997}

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