q^2+10q+10=0

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Solution for q^2+10q+10=0 equation: 


Simplifying
q2 + 10q + 10 = 0

Reorder the terms:
10 + 10q + q2 = 0

Solving
10 + 10q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 10q + -10 + q2 = 0 + -10

Reorder the terms:
10 + -10 + 10q + q2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 10q + q2 = 0 + -10
10q + q2 = 0 + -10

Combine like terms: 0 + -10 = -10
10q + q2 = -10

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 = -10 + 25

Reorder the terms:
25 + 10q + q2 = -10 + 25

Combine like terms: -10 + 25 = 15
25 + 10q + q2 = 15

Factor a perfect square on the left side:
(q + 5)(q + 5) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(q + 5) equal to 3.872983346 and -3.872983346.


Subproblem 1
q + 5 = 3.872983346

Simplifying
q + 5 = 3.872983346

Reorder the terms:
5 + q = 3.872983346

Solving
5 + q = 3.872983346

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 = 3.872983346 + -5

Combine like terms: 5 + -5 = 0
0 + q = 3.872983346 + -5
q = 3.872983346 + -5

Combine like terms: 3.872983346 + -5 = -1.127016654
q = -1.127016654

Simplifying
q = -1.127016654


Subproblem 2
q + 5 = -3.872983346

Simplifying
q + 5 = -3.872983346

Reorder the terms:
5 + q = -3.872983346

Solving
5 + q = -3.872983346

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 = -3.872983346 + -5

Combine like terms: 5 + -5 = 0
0 + q = -3.872983346 + -5
q = -3.872983346 + -5

Combine like terms: -3.872983346 + -5 = -8.872983346
q = -8.872983346

Simplifying
q = -8.872983346


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {-1.127016654, -8.872983346}

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