Q^2-180Q+400=0

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Solution for Q^2-180Q+400=0 equation: 


Simplifying
Q2 + -180Q + 400 = 0

Reorder the terms:
400 + -180Q + Q2 = 0

Solving
400 + -180Q + Q2 = 0

Solving for variable 'Q'.

Begin completing the square.

Move the constant term to the right:

Add '-400' to each side of the equation.
400 + -180Q + -400 + Q2 = 0 + -400

Reorder the terms:
400 + -400 + -180Q + Q2 = 0 + -400

Combine like terms: 400 + -400 = 0
0 + -180Q + Q2 = 0 + -400
-180Q + Q2 = 0 + -400

Combine like terms: 0 + -400 = -400
-180Q + Q2 = -400

The Q term is -180Q.  Take half its coefficient (-90).
Square it (8100) and add it to both sides.

Add '8100' to each side of the equation.
-180Q + 8100 + Q2 = -400 + 8100

Reorder the terms:
8100 + -180Q + Q2 = -400 + 8100

Combine like terms: -400 + 8100 = 7700
8100 + -180Q + Q2 = 7700

Factor a perfect square on the left side:
(Q + -90)(Q + -90) = 7700

Calculate the square root of the right side: 87.749643874

Break this problem into two subproblems by setting 
(Q + -90) equal to 87.749643874 and -87.749643874.


Subproblem 1
Q + -90 = 87.749643874

Simplifying
Q + -90 = 87.749643874

Reorder the terms:
-90 + Q = 87.749643874

Solving
-90 + Q = 87.749643874

Solving for variable 'Q'.

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

Add '90' to each side of the equation.
-90 + 90 + Q = 87.749643874 + 90

Combine like terms: -90 + 90 = 0
0 + Q = 87.749643874 + 90
Q = 87.749643874 + 90

Combine like terms: 87.749643874 + 90 = 177.749643874
Q = 177.749643874

Simplifying
Q = 177.749643874


Subproblem 2
Q + -90 = -87.749643874

Simplifying
Q + -90 = -87.749643874

Reorder the terms:
-90 + Q = -87.749643874

Solving
-90 + Q = -87.749643874

Solving for variable 'Q'.

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

Add '90' to each side of the equation.
-90 + 90 + Q = -87.749643874 + 90

Combine like terms: -90 + 90 = 0
0 + Q = -87.749643874 + 90
Q = -87.749643874 + 90

Combine like terms: -87.749643874 + 90 = 2.250356126
Q = 2.250356126

Simplifying
Q = 2.250356126


Solution
The solution to the problem is based on the solutions
from the subproblems.
Q = {177.749643874, 2.250356126}

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