2q^2+3q-8=q

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Solution for 2q^2+3q-8=q equation: 


Simplifying
2q2 + 3q + -8 = q

Reorder the terms:
-8 + 3q + 2q2 = q

Solving
-8 + 3q + 2q2 = q

Solving for variable 'q'.

Reorder the terms:
-8 + 3q + -1q + 2q2 = q + -1q

Combine like terms: 3q + -1q = 2q
-8 + 2q + 2q2 = q + -1q

Combine like terms: q + -1q = 0
-8 + 2q + 2q2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + q + q2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + q + q2)' equal to zero and attempt to solve:

Simplifying
-4 + q + q2 = 0

Solving
-4 + q + q2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The q term is q.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
q + 0.25 + q2 = 4 + 0.25

Reorder the terms:
0.25 + q + q2 = 4 + 0.25

Combine like terms: 4 + 0.25 = 4.25
0.25 + q + q2 = 4.25

Factor a perfect square on the left side:
(q + 0.5)(q + 0.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(q + 0.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
q + 0.5 = 2.061552813

Simplifying
q + 0.5 = 2.061552813

Reorder the terms:
0.5 + q = 2.061552813

Solving
0.5 + q = 2.061552813

Solving for variable 'q'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + q = 2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + q = 2.061552813 + -0.5
q = 2.061552813 + -0.5

Combine like terms: 2.061552813 + -0.5 = 1.561552813
q = 1.561552813

Simplifying
q = 1.561552813


Subproblem 2
q + 0.5 = -2.061552813

Simplifying
q + 0.5 = -2.061552813

Reorder the terms:
0.5 + q = -2.061552813

Solving
0.5 + q = -2.061552813

Solving for variable 'q'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + q = -2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + q = -2.061552813 + -0.5
q = -2.061552813 + -0.5

Combine like terms: -2.061552813 + -0.5 = -2.561552813
q = -2.561552813

Simplifying
q = -2.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {1.561552813, -2.561552813}
Solution
q = {1.561552813, -2.561552813}

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