2q^2-42q+100=0

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Solution for 2q^2-42q+100=0 equation: 


Simplifying
2q2 + -42q + 100 = 0

Reorder the terms:
100 + -42q + 2q2 = 0

Solving
100 + -42q + 2q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2'.
2(50 + -21q + q2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(50 + -21q + q2)' equal to zero and attempt to solve:

Simplifying
50 + -21q + q2 = 0

Solving
50 + -21q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-50' to each side of the equation.
50 + -21q + -50 + q2 = 0 + -50

Reorder the terms:
50 + -50 + -21q + q2 = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -21q + q2 = 0 + -50
-21q + q2 = 0 + -50

Combine like terms: 0 + -50 = -50
-21q + q2 = -50

The q term is -21q.  Take half its coefficient (-10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
-21q + 110.25 + q2 = -50 + 110.25

Reorder the terms:
110.25 + -21q + q2 = -50 + 110.25

Combine like terms: -50 + 110.25 = 60.25
110.25 + -21q + q2 = 60.25

Factor a perfect square on the left side:
(q + -10.5)(q + -10.5) = 60.25

Calculate the square root of the right side: 7.762087348

Break this problem into two subproblems by setting 
(q + -10.5) equal to 7.762087348 and -7.762087348.


Subproblem 1
q + -10.5 = 7.762087348

Simplifying
q + -10.5 = 7.762087348

Reorder the terms:
-10.5 + q = 7.762087348

Solving
-10.5 + q = 7.762087348

Solving for variable 'q'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + q = 7.762087348 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + q = 7.762087348 + 10.5
q = 7.762087348 + 10.5

Combine like terms: 7.762087348 + 10.5 = 18.262087348
q = 18.262087348

Simplifying
q = 18.262087348


Subproblem 2
q + -10.5 = -7.762087348

Simplifying
q + -10.5 = -7.762087348

Reorder the terms:
-10.5 + q = -7.762087348

Solving
-10.5 + q = -7.762087348

Solving for variable 'q'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + q = -7.762087348 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + q = -7.762087348 + 10.5
q = -7.762087348 + 10.5

Combine like terms: -7.762087348 + 10.5 = 2.737912652
q = 2.737912652

Simplifying
q = 2.737912652


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {18.262087348, 2.737912652}
Solution
q = {18.262087348, 2.737912652}

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