Q^2+22Q+60=0

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Solution for Q^2+22Q+60=0 equation: 


Simplifying
Q2 + 22Q + 60 = 0

Reorder the terms:
60 + 22Q + Q2 = 0

Solving
60 + 22Q + Q2 = 0

Solving for variable 'Q'.

Begin completing the square.

Move the constant term to the right:

Add '-60' to each side of the equation.
60 + 22Q + -60 + Q2 = 0 + -60

Reorder the terms:
60 + -60 + 22Q + Q2 = 0 + -60

Combine like terms: 60 + -60 = 0
0 + 22Q + Q2 = 0 + -60
22Q + Q2 = 0 + -60

Combine like terms: 0 + -60 = -60
22Q + Q2 = -60

The Q term is 22Q.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22Q + 121 + Q2 = -60 + 121

Reorder the terms:
121 + 22Q + Q2 = -60 + 121

Combine like terms: -60 + 121 = 61
121 + 22Q + Q2 = 61

Factor a perfect square on the left side:
(Q + 11)(Q + 11) = 61

Calculate the square root of the right side: 7.810249676

Break this problem into two subproblems by setting 
(Q + 11) equal to 7.810249676 and -7.810249676.


Subproblem 1
Q + 11 = 7.810249676

Simplifying
Q + 11 = 7.810249676

Reorder the terms:
11 + Q = 7.810249676

Solving
11 + Q = 7.810249676

Solving for variable 'Q'.

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

Add '-11' to each side of the equation.
11 + -11 + Q = 7.810249676 + -11

Combine like terms: 11 + -11 = 0
0 + Q = 7.810249676 + -11
Q = 7.810249676 + -11

Combine like terms: 7.810249676 + -11 = -3.189750324
Q = -3.189750324

Simplifying
Q = -3.189750324


Subproblem 2
Q + 11 = -7.810249676

Simplifying
Q + 11 = -7.810249676

Reorder the terms:
11 + Q = -7.810249676

Solving
11 + Q = -7.810249676

Solving for variable 'Q'.

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

Add '-11' to each side of the equation.
11 + -11 + Q = -7.810249676 + -11

Combine like terms: 11 + -11 = 0
0 + Q = -7.810249676 + -11
Q = -7.810249676 + -11

Combine like terms: -7.810249676 + -11 = -18.810249676
Q = -18.810249676

Simplifying
Q = -18.810249676


Solution
The solution to the problem is based on the solutions
from the subproblems.
Q = {-3.189750324, -18.810249676}

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