v^2-30v-17=0

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Solution for v^2-30v-17=0 equation: 


Simplifying
v2 + -30v + -17 = 0

Reorder the terms:
-17 + -30v + v2 = 0

Solving
-17 + -30v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -30v + 17 + v2 = 0 + 17

Reorder the terms:
-17 + 17 + -30v + v2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -30v + v2 = 0 + 17
-30v + v2 = 0 + 17

Combine like terms: 0 + 17 = 17
-30v + v2 = 17

The v term is -30v.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30v + 225 + v2 = 17 + 225

Reorder the terms:
225 + -30v + v2 = 17 + 225

Combine like terms: 17 + 225 = 242
225 + -30v + v2 = 242

Factor a perfect square on the left side:
(v + -15)(v + -15) = 242

Calculate the square root of the right side: 15.556349186

Break this problem into two subproblems by setting 
(v + -15) equal to 15.556349186 and -15.556349186.


Subproblem 1
v + -15 = 15.556349186

Simplifying
v + -15 = 15.556349186

Reorder the terms:
-15 + v = 15.556349186

Solving
-15 + v = 15.556349186

Solving for variable 'v'.

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

Add '15' to each side of the equation.
-15 + 15 + v = 15.556349186 + 15

Combine like terms: -15 + 15 = 0
0 + v = 15.556349186 + 15
v = 15.556349186 + 15

Combine like terms: 15.556349186 + 15 = 30.556349186
v = 30.556349186

Simplifying
v = 30.556349186


Subproblem 2
v + -15 = -15.556349186

Simplifying
v + -15 = -15.556349186

Reorder the terms:
-15 + v = -15.556349186

Solving
-15 + v = -15.556349186

Solving for variable 'v'.

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

Add '15' to each side of the equation.
-15 + 15 + v = -15.556349186 + 15

Combine like terms: -15 + 15 = 0
0 + v = -15.556349186 + 15
v = -15.556349186 + 15

Combine like terms: -15.556349186 + 15 = -0.556349186
v = -0.556349186

Simplifying
v = -0.556349186


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {30.556349186, -0.556349186}

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