q^2-7q-12=0

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Solution for q^2-7q-12=0 equation: 


Simplifying
q2 + -7q + -12 = 0

Reorder the terms:
-12 + -7q + q2 = 0

Solving
-12 + -7q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -7q + 12 + q2 = 0 + 12

Reorder the terms:
-12 + 12 + -7q + q2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -7q + q2 = 0 + 12
-7q + q2 = 0 + 12

Combine like terms: 0 + 12 = 12
-7q + q2 = 12

The q term is -7q.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7q + 12.25 + q2 = 12 + 12.25

Reorder the terms:
12.25 + -7q + q2 = 12 + 12.25

Combine like terms: 12 + 12.25 = 24.25
12.25 + -7q + q2 = 24.25

Factor a perfect square on the left side:
(q + -3.5)(q + -3.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(q + -3.5) equal to 4.924428901 and -4.924428901.


Subproblem 1
q + -3.5 = 4.924428901

Simplifying
q + -3.5 = 4.924428901

Reorder the terms:
-3.5 + q = 4.924428901

Solving
-3.5 + q = 4.924428901

Solving for variable 'q'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + q = 4.924428901 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + q = 4.924428901 + 3.5
q = 4.924428901 + 3.5

Combine like terms: 4.924428901 + 3.5 = 8.424428901
q = 8.424428901

Simplifying
q = 8.424428901


Subproblem 2
q + -3.5 = -4.924428901

Simplifying
q + -3.5 = -4.924428901

Reorder the terms:
-3.5 + q = -4.924428901

Solving
-3.5 + q = -4.924428901

Solving for variable 'q'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + q = -4.924428901 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + q = -4.924428901 + 3.5
q = -4.924428901 + 3.5

Combine like terms: -4.924428901 + 3.5 = -1.424428901
q = -1.424428901

Simplifying
q = -1.424428901


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {8.424428901, -1.424428901}

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