3q^2-12q+18=20

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Solution for 3q^2-12q+18=20 equation:


Simplifying
3q2 + -12q + 18 = 20

Reorder the terms:
18 + -12q + 3q2 = 20

Solving
18 + -12q + 3q2 = 20

Solving for variable 'q'.

Reorder the terms:
18 + -20 + -12q + 3q2 = 20 + -20

Combine like terms: 18 + -20 = -2
-2 + -12q + 3q2 = 20 + -20

Combine like terms: 20 + -20 = 0
-2 + -12q + 3q2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-0.6666666667 + -4q + q2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -4q + 0.6666666667 + q2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -4q + q2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -4q + q2 = 0 + 0.6666666667
-4q + q2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-4q + q2 = 0.6666666667

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 = 0.6666666667 + 4

Reorder the terms:
4 + -4q + q2 = 0.6666666667 + 4

Combine like terms: 0.6666666667 + 4 = 4.6666666667
4 + -4q + q2 = 4.6666666667

Factor a perfect square on the left side:
(q + -2)(q + -2) = 4.6666666667

Calculate the square root of the right side: 2.160246899

Break this problem into two subproblems by setting 
(q + -2) equal to 2.160246899 and -2.160246899.

Subproblem 1

q + -2 = 2.160246899 Simplifying q + -2 = 2.160246899 Reorder the terms: -2 + q = 2.160246899 Solving -2 + q = 2.160246899 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 = 2.160246899 + 2 Combine like terms: -2 + 2 = 0 0 + q = 2.160246899 + 2 q = 2.160246899 + 2 Combine like terms: 2.160246899 + 2 = 4.160246899 q = 4.160246899 Simplifying q = 4.160246899

Subproblem 2

q + -2 = -2.160246899 Simplifying q + -2 = -2.160246899 Reorder the terms: -2 + q = -2.160246899 Solving -2 + q = -2.160246899 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 = -2.160246899 + 2 Combine like terms: -2 + 2 = 0 0 + q = -2.160246899 + 2 q = -2.160246899 + 2 Combine like terms: -2.160246899 + 2 = -0.160246899 q = -0.160246899 Simplifying q = -0.160246899

Solution

The solution to the problem is based on the solutions from the subproblems. q = {4.160246899, -0.160246899}

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