5v^2-30v+4=

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Solution for 5v^2-30v+4= equation:


Simplifying
5v2 + -30v + 4 = 0

Reorder the terms:
4 + -30v + 5v2 = 0

Solving
4 + -30v + 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'.
0.8 + -6v + v2 = 0

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + -6v + -0.8 + v2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + -6v + v2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + -6v + v2 = 0 + -0.8
-6v + v2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
-6v + v2 = -0.8

The v term is -6v.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6v + 9 + v2 = -0.8 + 9

Reorder the terms:
9 + -6v + v2 = -0.8 + 9

Combine like terms: -0.8 + 9 = 8.2
9 + -6v + v2 = 8.2

Factor a perfect square on the left side:
(v + -3)(v + -3) = 8.2

Calculate the square root of the right side: 2.863564213

Break this problem into two subproblems by setting 
(v + -3) equal to 2.863564213 and -2.863564213.

Subproblem 1

v + -3 = 2.863564213 Simplifying v + -3 = 2.863564213 Reorder the terms: -3 + v = 2.863564213 Solving -3 + v = 2.863564213 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + v = 2.863564213 + 3 Combine like terms: -3 + 3 = 0 0 + v = 2.863564213 + 3 v = 2.863564213 + 3 Combine like terms: 2.863564213 + 3 = 5.863564213 v = 5.863564213 Simplifying v = 5.863564213

Subproblem 2

v + -3 = -2.863564213 Simplifying v + -3 = -2.863564213 Reorder the terms: -3 + v = -2.863564213 Solving -3 + v = -2.863564213 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + v = -2.863564213 + 3 Combine like terms: -3 + 3 = 0 0 + v = -2.863564213 + 3 v = -2.863564213 + 3 Combine like terms: -2.863564213 + 3 = 0.136435787 v = 0.136435787 Simplifying v = 0.136435787

Solution

The solution to the problem is based on the solutions from the subproblems. v = {5.863564213, 0.136435787}

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