q^2-9q+7=0

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Solution for q^2-9q+7=0 equation: 


Simplifying
q2 + -9q + 7 = 0

Reorder the terms:
7 + -9q + q2 = 0

Solving
7 + -9q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -9q + -7 + q2 = 0 + -7

Reorder the terms:
7 + -7 + -9q + q2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -9q + q2 = 0 + -7
-9q + q2 = 0 + -7

Combine like terms: 0 + -7 = -7
-9q + q2 = -7

The q term is -9q.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9q + 20.25 + q2 = -7 + 20.25

Reorder the terms:
20.25 + -9q + q2 = -7 + 20.25

Combine like terms: -7 + 20.25 = 13.25
20.25 + -9q + q2 = 13.25

Factor a perfect square on the left side:
(q + -4.5)(q + -4.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(q + -4.5) equal to 3.640054945 and -3.640054945.


Subproblem 1
q + -4.5 = 3.640054945

Simplifying
q + -4.5 = 3.640054945

Reorder the terms:
-4.5 + q = 3.640054945

Solving
-4.5 + q = 3.640054945

Solving for variable 'q'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + q = 3.640054945 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + q = 3.640054945 + 4.5
q = 3.640054945 + 4.5

Combine like terms: 3.640054945 + 4.5 = 8.140054945
q = 8.140054945

Simplifying
q = 8.140054945


Subproblem 2
q + -4.5 = -3.640054945

Simplifying
q + -4.5 = -3.640054945

Reorder the terms:
-4.5 + q = -3.640054945

Solving
-4.5 + q = -3.640054945

Solving for variable 'q'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + q = -3.640054945 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + q = -3.640054945 + 4.5
q = -3.640054945 + 4.5

Combine like terms: -3.640054945 + 4.5 = 0.859945055
q = 0.859945055

Simplifying
q = 0.859945055


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {8.140054945, 0.859945055}

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