q^2-4q+6=10

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Solution for q^2-4q+6=10 equation: 


Simplifying
q2 + -4q + 6 = 10

Reorder the terms:
6 + -4q + q2 = 10

Solving
6 + -4q + q2 = 10

Solving for variable 'q'.

Reorder the terms:
6 + -10 + -4q + q2 = 10 + -10

Combine like terms: 6 + -10 = -4
-4 + -4q + q2 = 10 + -10

Combine like terms: 10 + -10 = 0
-4 + -4q + q2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The q term is -4q.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

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

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

Combine like terms: 4 + 4 = 8
4 + -4q + q2 = 8

Factor a perfect square on the left side:
(q + -2)(q + -2) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(q + -2) equal to 2.828427125 and -2.828427125.


Subproblem 1
q + -2 = 2.828427125

Simplifying
q + -2 = 2.828427125

Reorder the terms:
-2 + q = 2.828427125

Solving
-2 + q = 2.828427125

Solving for variable 'q'.

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

Add '2' to each side of the equation.
-2 + 2 + q = 2.828427125 + 2

Combine like terms: -2 + 2 = 0
0 + q = 2.828427125 + 2
q = 2.828427125 + 2

Combine like terms: 2.828427125 + 2 = 4.828427125
q = 4.828427125

Simplifying
q = 4.828427125


Subproblem 2
q + -2 = -2.828427125

Simplifying
q + -2 = -2.828427125

Reorder the terms:
-2 + q = -2.828427125

Solving
-2 + q = -2.828427125

Solving for variable 'q'.

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

Add '2' to each side of the equation.
-2 + 2 + q = -2.828427125 + 2

Combine like terms: -2 + 2 = 0
0 + q = -2.828427125 + 2
q = -2.828427125 + 2

Combine like terms: -2.828427125 + 2 = -0.828427125
q = -0.828427125

Simplifying
q = -0.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {4.828427125, -0.828427125}

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