q^2-30q+40=0

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Solution for q^2-30q+40=0 equation: 


Simplifying
q2 + -30q + 40 = 0

Reorder the terms:
40 + -30q + q2 = 0

Solving
40 + -30q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + -30q + -40 + q2 = 0 + -40

Reorder the terms:
40 + -40 + -30q + q2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -30q + q2 = 0 + -40
-30q + q2 = 0 + -40

Combine like terms: 0 + -40 = -40
-30q + q2 = -40

The q term is -30q.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30q + 225 + q2 = -40 + 225

Reorder the terms:
225 + -30q + q2 = -40 + 225

Combine like terms: -40 + 225 = 185
225 + -30q + q2 = 185

Factor a perfect square on the left side:
(q + -15)(q + -15) = 185

Calculate the square root of the right side: 13.601470509

Break this problem into two subproblems by setting 
(q + -15) equal to 13.601470509 and -13.601470509.


Subproblem 1
q + -15 = 13.601470509

Simplifying
q + -15 = 13.601470509

Reorder the terms:
-15 + q = 13.601470509

Solving
-15 + q = 13.601470509

Solving for variable 'q'.

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

Add '15' to each side of the equation.
-15 + 15 + q = 13.601470509 + 15

Combine like terms: -15 + 15 = 0
0 + q = 13.601470509 + 15
q = 13.601470509 + 15

Combine like terms: 13.601470509 + 15 = 28.601470509
q = 28.601470509

Simplifying
q = 28.601470509


Subproblem 2
q + -15 = -13.601470509

Simplifying
q + -15 = -13.601470509

Reorder the terms:
-15 + q = -13.601470509

Solving
-15 + q = -13.601470509

Solving for variable 'q'.

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

Add '15' to each side of the equation.
-15 + 15 + q = -13.601470509 + 15

Combine like terms: -15 + 15 = 0
0 + q = -13.601470509 + 15
q = -13.601470509 + 15

Combine like terms: -13.601470509 + 15 = 1.398529491
q = 1.398529491

Simplifying
q = 1.398529491


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {28.601470509, 1.398529491}

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