0=v^2-9v-8

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Solution for 0=v^2-9v-8 equation:


Simplifying
0 = v2 + -9v + -8

Reorder the terms:
0 = -8 + -9v + v2

Solving
0 = -8 + -9v + v2

Solving for variable 'v'.

Combine like terms: 0 + 8 = 8
8 + 9v + -1v2 = -8 + -9v + v2 + 8 + 9v + -1v2

Reorder the terms:
8 + 9v + -1v2 = -8 + 8 + -9v + 9v + v2 + -1v2

Combine like terms: -8 + 8 = 0
8 + 9v + -1v2 = 0 + -9v + 9v + v2 + -1v2
8 + 9v + -1v2 = -9v + 9v + v2 + -1v2

Combine like terms: -9v + 9v = 0
8 + 9v + -1v2 = 0 + v2 + -1v2
8 + 9v + -1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
8 + 9v + -1v2 = 0

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

Divide each side by '-1'.
-8 + -9v + v2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -9v + 8 + v2 = 0 + 8

Reorder the terms:
-8 + 8 + -9v + v2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -9v + v2 = 0 + 8
-9v + v2 = 0 + 8

Combine like terms: 0 + 8 = 8
-9v + v2 = 8

The v term is -9v.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9v + 20.25 + v2 = 8 + 20.25

Reorder the terms:
20.25 + -9v + v2 = 8 + 20.25

Combine like terms: 8 + 20.25 = 28.25
20.25 + -9v + v2 = 28.25

Factor a perfect square on the left side:
(v + -4.5)(v + -4.5) = 28.25

Calculate the square root of the right side: 5.315072906

Break this problem into two subproblems by setting 
(v + -4.5) equal to 5.315072906 and -5.315072906.

Subproblem 1

v + -4.5 = 5.315072906 Simplifying v + -4.5 = 5.315072906 Reorder the terms: -4.5 + v = 5.315072906 Solving -4.5 + v = 5.315072906 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + v = 5.315072906 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + v = 5.315072906 + 4.5 v = 5.315072906 + 4.5 Combine like terms: 5.315072906 + 4.5 = 9.815072906 v = 9.815072906 Simplifying v = 9.815072906

Subproblem 2

v + -4.5 = -5.315072906 Simplifying v + -4.5 = -5.315072906 Reorder the terms: -4.5 + v = -5.315072906 Solving -4.5 + v = -5.315072906 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + v = -5.315072906 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + v = -5.315072906 + 4.5 v = -5.315072906 + 4.5 Combine like terms: -5.315072906 + 4.5 = -0.815072906 v = -0.815072906 Simplifying v = -0.815072906

Solution

The solution to the problem is based on the solutions from the subproblems. v = {9.815072906, -0.815072906}

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