v^2-12v+24=0

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Solution for v^2-12v+24=0 equation:


Simplifying
v2 + -12v + 24 = 0

Reorder the terms:
24 + -12v + v2 = 0

Solving
24 + -12v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -12v + -24 + v2 = 0 + -24

Reorder the terms:
24 + -24 + -12v + v2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -12v + v2 = 0 + -24
-12v + v2 = 0 + -24

Combine like terms: 0 + -24 = -24
-12v + v2 = -24

The v term is -12v.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12v + 36 + v2 = -24 + 36

Reorder the terms:
36 + -12v + v2 = -24 + 36

Combine like terms: -24 + 36 = 12
36 + -12v + v2 = 12

Factor a perfect square on the left side:
(v + -6)(v + -6) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(v + -6) equal to 3.464101615 and -3.464101615.

Subproblem 1

v + -6 = 3.464101615 Simplifying v + -6 = 3.464101615 Reorder the terms: -6 + v = 3.464101615 Solving -6 + v = 3.464101615 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + v = 3.464101615 + 6 Combine like terms: -6 + 6 = 0 0 + v = 3.464101615 + 6 v = 3.464101615 + 6 Combine like terms: 3.464101615 + 6 = 9.464101615 v = 9.464101615 Simplifying v = 9.464101615

Subproblem 2

v + -6 = -3.464101615 Simplifying v + -6 = -3.464101615 Reorder the terms: -6 + v = -3.464101615 Solving -6 + v = -3.464101615 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + v = -3.464101615 + 6 Combine like terms: -6 + 6 = 0 0 + v = -3.464101615 + 6 v = -3.464101615 + 6 Combine like terms: -3.464101615 + 6 = 2.535898385 v = 2.535898385 Simplifying v = 2.535898385

Solution

The solution to the problem is based on the solutions from the subproblems. v = {9.464101615, 2.535898385}

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