Q^2+10Q+5=0

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Solution for Q^2+10Q+5=0 equation: 


Simplifying
Q2 + 10Q + 5 = 0

Reorder the terms:
5 + 10Q + Q2 = 0

Solving
5 + 10Q + Q2 = 0

Solving for variable 'Q'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 10Q + -5 + Q2 = 0 + -5

Reorder the terms:
5 + -5 + 10Q + Q2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 10Q + Q2 = 0 + -5
10Q + Q2 = 0 + -5

Combine like terms: 0 + -5 = -5
10Q + Q2 = -5

The Q term is 10Q.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10Q + 25 + Q2 = -5 + 25

Reorder the terms:
25 + 10Q + Q2 = -5 + 25

Combine like terms: -5 + 25 = 20
25 + 10Q + Q2 = 20

Factor a perfect square on the left side:
(Q + 5)(Q + 5) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(Q + 5) equal to 4.472135955 and -4.472135955.


Subproblem 1
Q + 5 = 4.472135955

Simplifying
Q + 5 = 4.472135955

Reorder the terms:
5 + Q = 4.472135955

Solving
5 + Q = 4.472135955

Solving for variable 'Q'.

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

Add '-5' to each side of the equation.
5 + -5 + Q = 4.472135955 + -5

Combine like terms: 5 + -5 = 0
0 + Q = 4.472135955 + -5
Q = 4.472135955 + -5

Combine like terms: 4.472135955 + -5 = -0.527864045
Q = -0.527864045

Simplifying
Q = -0.527864045


Subproblem 2
Q + 5 = -4.472135955

Simplifying
Q + 5 = -4.472135955

Reorder the terms:
5 + Q = -4.472135955

Solving
5 + Q = -4.472135955

Solving for variable 'Q'.

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

Add '-5' to each side of the equation.
5 + -5 + Q = -4.472135955 + -5

Combine like terms: 5 + -5 = 0
0 + Q = -4.472135955 + -5
Q = -4.472135955 + -5

Combine like terms: -4.472135955 + -5 = -9.472135955
Q = -9.472135955

Simplifying
Q = -9.472135955


Solution
The solution to the problem is based on the solutions
from the subproblems.
Q = {-0.527864045, -9.472135955}

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