2(2q+1)=q^2

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Solution for 2(2q+1)=q^2 equation: 


Simplifying
2(2q + 1) = q2

Reorder the terms:
2(1 + 2q) = q2
(1 * 2 + 2q * 2) = q2
(2 + 4q) = q2

Solving
2 + 4q = q2

Solving for variable 'q'.

Combine like terms: q2 + -1q2 = 0
2 + 4q + -1q2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2 + -4q + q2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -4q + 2 + q2 = 0 + 2

Reorder the terms:
-2 + 2 + -4q + q2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -4q + q2 = 0 + 2
-4q + q2 = 0 + 2

Combine like terms: 0 + 2 = 2
-4q + q2 = 2

The q term is -4q.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4q + 4 + q2 = 2 + 4

Reorder the terms:
4 + -4q + q2 = 2 + 4

Combine like terms: 2 + 4 = 6
4 + -4q + q2 = 6

Factor a perfect square on the left side:
(q + -2)(q + -2) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(q + -2) equal to 2.449489743 and -2.449489743.


Subproblem 1
q + -2 = 2.449489743

Simplifying
q + -2 = 2.449489743

Reorder the terms:
-2 + q = 2.449489743

Solving
-2 + q = 2.449489743

Solving for variable 'q'.

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

Add '2' to each side of the equation.
-2 + 2 + q = 2.449489743 + 2

Combine like terms: -2 + 2 = 0
0 + q = 2.449489743 + 2
q = 2.449489743 + 2

Combine like terms: 2.449489743 + 2 = 4.449489743
q = 4.449489743

Simplifying
q = 4.449489743


Subproblem 2
q + -2 = -2.449489743

Simplifying
q + -2 = -2.449489743

Reorder the terms:
-2 + q = -2.449489743

Solving
-2 + q = -2.449489743

Solving for variable 'q'.

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

Add '2' to each side of the equation.
-2 + 2 + q = -2.449489743 + 2

Combine like terms: -2 + 2 = 0
0 + q = -2.449489743 + 2
q = -2.449489743 + 2

Combine like terms: -2.449489743 + 2 = -0.449489743
q = -0.449489743

Simplifying
q = -0.449489743


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {4.449489743, -0.449489743}

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