q^2-7q+2=0

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


Simplifying
q2 + -7q + 2 = 0

Reorder the terms:
2 + -7q + q2 = 0

Solving
2 + -7q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -7q + -2 + q2 = 0 + -2

Reorder the terms:
2 + -2 + -7q + q2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7q + q2 = 0 + -2
-7q + q2 = 0 + -2

Combine like terms: 0 + -2 = -2
-7q + q2 = -2

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 = -2 + 12.25

Reorder the terms:
12.25 + -7q + q2 = -2 + 12.25

Combine like terms: -2 + 12.25 = 10.25
12.25 + -7q + q2 = 10.25

Factor a perfect square on the left side:
(q + -3.5)(q + -3.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(q + -3.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
q + -3.5 = 3.201562119

Simplifying
q + -3.5 = 3.201562119

Reorder the terms:
-3.5 + q = 3.201562119

Solving
-3.5 + q = 3.201562119

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 = 3.201562119 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + q = 3.201562119 + 3.5
q = 3.201562119 + 3.5

Combine like terms: 3.201562119 + 3.5 = 6.701562119
q = 6.701562119

Simplifying
q = 6.701562119


Subproblem 2
q + -3.5 = -3.201562119

Simplifying
q + -3.5 = -3.201562119

Reorder the terms:
-3.5 + q = -3.201562119

Solving
-3.5 + q = -3.201562119

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 = -3.201562119 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + q = -3.201562119 + 3.5
q = -3.201562119 + 3.5

Combine like terms: -3.201562119 + 3.5 = 0.298437881
q = 0.298437881

Simplifying
q = 0.298437881


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {6.701562119, 0.298437881}

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