q=2+(q+8)(q+3)

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Solution for q=2+(q+8)(q+3) equation:


Simplifying
q = 2 + (q + 8)(q + 3)

Reorder the terms:
q = 2 + (8 + q)(q + 3)

Reorder the terms:
q = 2 + (8 + q)(3 + q)

Multiply (8 + q) * (3 + q)
q = 2 + (8(3 + q) + q(3 + q))
q = 2 + ((3 * 8 + q * 8) + q(3 + q))
q = 2 + ((24 + 8q) + q(3 + q))
q = 2 + (24 + 8q + (3 * q + q * q))
q = 2 + (24 + 8q + (3q + q2))

Combine like terms: 8q + 3q = 11q
q = 2 + (24 + 11q + q2)

Combine like terms: 2 + 24 = 26
q = 26 + 11q + q2

Solving
q = 26 + 11q + q2

Solving for variable 'q'.

Reorder the terms:
-26 + q + -11q + -1q2 = 26 + 11q + q2 + -26 + -11q + -1q2

Combine like terms: q + -11q = -10q
-26 + -10q + -1q2 = 26 + 11q + q2 + -26 + -11q + -1q2

Reorder the terms:
-26 + -10q + -1q2 = 26 + -26 + 11q + -11q + q2 + -1q2

Combine like terms: 26 + -26 = 0
-26 + -10q + -1q2 = 0 + 11q + -11q + q2 + -1q2
-26 + -10q + -1q2 = 11q + -11q + q2 + -1q2

Combine like terms: 11q + -11q = 0
-26 + -10q + -1q2 = 0 + q2 + -1q2
-26 + -10q + -1q2 = q2 + -1q2

Combine like terms: q2 + -1q2 = 0
-26 + -10q + -1q2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(26 + 10q + q2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(26 + 10q + q2)' equal to zero and attempt to solve:

Simplifying
26 + 10q + q2 = 0

Solving
26 + 10q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-26' to each side of the equation.
26 + 10q + -26 + q2 = 0 + -26

Reorder the terms:
26 + -26 + 10q + q2 = 0 + -26

Combine like terms: 26 + -26 = 0
0 + 10q + q2 = 0 + -26
10q + q2 = 0 + -26

Combine like terms: 0 + -26 = -26
10q + q2 = -26

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 = -26 + 25

Reorder the terms:
25 + 10q + q2 = -26 + 25

Combine like terms: -26 + 25 = -1
25 + 10q + q2 = -1

Factor a perfect square on the left side:
(q + 5)(q + 5) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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