q^2-8q-21=0

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Solution for q^2-8q-21=0 equation: 


Simplifying
q2 + -8q + -21 = 0

Reorder the terms:
-21 + -8q + q2 = 0

Solving
-21 + -8q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + -8q + 21 + q2 = 0 + 21

Reorder the terms:
-21 + 21 + -8q + q2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -8q + q2 = 0 + 21
-8q + q2 = 0 + 21

Combine like terms: 0 + 21 = 21
-8q + q2 = 21

The q term is -8q.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8q + 16 + q2 = 21 + 16

Reorder the terms:
16 + -8q + q2 = 21 + 16

Combine like terms: 21 + 16 = 37
16 + -8q + q2 = 37

Factor a perfect square on the left side:
(q + -4)(q + -4) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(q + -4) equal to 6.08276253 and -6.08276253.


Subproblem 1
q + -4 = 6.08276253

Simplifying
q + -4 = 6.08276253

Reorder the terms:
-4 + q = 6.08276253

Solving
-4 + q = 6.08276253

Solving for variable 'q'.

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

Add '4' to each side of the equation.
-4 + 4 + q = 6.08276253 + 4

Combine like terms: -4 + 4 = 0
0 + q = 6.08276253 + 4
q = 6.08276253 + 4

Combine like terms: 6.08276253 + 4 = 10.08276253
q = 10.08276253

Simplifying
q = 10.08276253


Subproblem 2
q + -4 = -6.08276253

Simplifying
q + -4 = -6.08276253

Reorder the terms:
-4 + q = -6.08276253

Solving
-4 + q = -6.08276253

Solving for variable 'q'.

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

Add '4' to each side of the equation.
-4 + 4 + q = -6.08276253 + 4

Combine like terms: -4 + 4 = 0
0 + q = -6.08276253 + 4
q = -6.08276253 + 4

Combine like terms: -6.08276253 + 4 = -2.08276253
q = -2.08276253

Simplifying
q = -2.08276253


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {10.08276253, -2.08276253}

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