v^2-18v+27=0

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Solution for v^2-18v+27=0 equation:


Simplifying
v2 + -18v + 27 = 0

Reorder the terms:
27 + -18v + v2 = 0

Solving
27 + -18v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + -18v + -27 + v2 = 0 + -27

Reorder the terms:
27 + -27 + -18v + v2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -18v + v2 = 0 + -27
-18v + v2 = 0 + -27

Combine like terms: 0 + -27 = -27
-18v + v2 = -27

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 = -27 + 81

Reorder the terms:
81 + -18v + v2 = -27 + 81

Combine like terms: -27 + 81 = 54
81 + -18v + v2 = 54

Factor a perfect square on the left side:
(v + -9)(v + -9) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(v + -9) equal to 7.348469228 and -7.348469228.

Subproblem 1

v + -9 = 7.348469228 Simplifying v + -9 = 7.348469228 Reorder the terms: -9 + v = 7.348469228 Solving -9 + v = 7.348469228 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 = 7.348469228 + 9 Combine like terms: -9 + 9 = 0 0 + v = 7.348469228 + 9 v = 7.348469228 + 9 Combine like terms: 7.348469228 + 9 = 16.348469228 v = 16.348469228 Simplifying v = 16.348469228

Subproblem 2

v + -9 = -7.348469228 Simplifying v + -9 = -7.348469228 Reorder the terms: -9 + v = -7.348469228 Solving -9 + v = -7.348469228 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 = -7.348469228 + 9 Combine like terms: -9 + 9 = 0 0 + v = -7.348469228 + 9 v = -7.348469228 + 9 Combine like terms: -7.348469228 + 9 = 1.651530772 v = 1.651530772 Simplifying v = 1.651530772

Solution

The solution to the problem is based on the solutions from the subproblems. v = {16.348469228, 1.651530772}

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