v^2-18v+21=0

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Solution for v^2-18v+21=0 equation:


Simplifying
v2 + -18v + 21 = 0

Reorder the terms:
21 + -18v + v2 = 0

Solving
21 + -18v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + -18v + -21 + v2 = 0 + -21

Reorder the terms:
21 + -21 + -18v + v2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -18v + v2 = 0 + -21
-18v + v2 = 0 + -21

Combine like terms: 0 + -21 = -21
-18v + v2 = -21

The v term is -18v.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18v + 81 + v2 = -21 + 81

Reorder the terms:
81 + -18v + v2 = -21 + 81

Combine like terms: -21 + 81 = 60
81 + -18v + v2 = 60

Factor a perfect square on the left side:
(v + -9)(v + -9) = 60

Calculate the square root of the right side: 7.745966692

Break this problem into two subproblems by setting 
(v + -9) equal to 7.745966692 and -7.745966692.

Subproblem 1

v + -9 = 7.745966692 Simplifying v + -9 = 7.745966692 Reorder the terms: -9 + v = 7.745966692 Solving -9 + v = 7.745966692 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + v = 7.745966692 + 9 Combine like terms: -9 + 9 = 0 0 + v = 7.745966692 + 9 v = 7.745966692 + 9 Combine like terms: 7.745966692 + 9 = 16.745966692 v = 16.745966692 Simplifying v = 16.745966692

Subproblem 2

v + -9 = -7.745966692 Simplifying v + -9 = -7.745966692 Reorder the terms: -9 + v = -7.745966692 Solving -9 + v = -7.745966692 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + v = -7.745966692 + 9 Combine like terms: -9 + 9 = 0 0 + v = -7.745966692 + 9 v = -7.745966692 + 9 Combine like terms: -7.745966692 + 9 = 1.254033308 v = 1.254033308 Simplifying v = 1.254033308

Solution

The solution to the problem is based on the solutions from the subproblems. v = {16.745966692, 1.254033308}

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