4q^2+3q=3q^2-9q+18

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Solution for 4q^2+3q=3q^2-9q+18 equation:


Simplifying
4q2 + 3q = 3q2 + -9q + 18

Reorder the terms:
3q + 4q2 = 3q2 + -9q + 18

Reorder the terms:
3q + 4q2 = 18 + -9q + 3q2

Solving
3q + 4q2 = 18 + -9q + 3q2

Solving for variable 'q'.

Reorder the terms:
-18 + 3q + 9q + 4q2 + -3q2 = 18 + -9q + 3q2 + -18 + 9q + -3q2

Combine like terms: 3q + 9q = 12q
-18 + 12q + 4q2 + -3q2 = 18 + -9q + 3q2 + -18 + 9q + -3q2

Combine like terms: 4q2 + -3q2 = 1q2
-18 + 12q + 1q2 = 18 + -9q + 3q2 + -18 + 9q + -3q2

Reorder the terms:
-18 + 12q + 1q2 = 18 + -18 + -9q + 9q + 3q2 + -3q2

Combine like terms: 18 + -18 = 0
-18 + 12q + 1q2 = 0 + -9q + 9q + 3q2 + -3q2
-18 + 12q + 1q2 = -9q + 9q + 3q2 + -3q2

Combine like terms: -9q + 9q = 0
-18 + 12q + 1q2 = 0 + 3q2 + -3q2
-18 + 12q + 1q2 = 3q2 + -3q2

Combine like terms: 3q2 + -3q2 = 0
-18 + 12q + 1q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 12q + 18 + q2 = 0 + 18

Reorder the terms:
-18 + 18 + 12q + q2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 12q + q2 = 0 + 18
12q + q2 = 0 + 18

Combine like terms: 0 + 18 = 18
12q + q2 = 18

The q term is 12q.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12q + 36 + q2 = 18 + 36

Reorder the terms:
36 + 12q + q2 = 18 + 36

Combine like terms: 18 + 36 = 54
36 + 12q + q2 = 54

Factor a perfect square on the left side:
(q + 6)(q + 6) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(q + 6) equal to 7.348469228 and -7.348469228.

Subproblem 1

q + 6 = 7.348469228 Simplifying q + 6 = 7.348469228 Reorder the terms: 6 + q = 7.348469228 Solving 6 + q = 7.348469228 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + q = 7.348469228 + -6 Combine like terms: 6 + -6 = 0 0 + q = 7.348469228 + -6 q = 7.348469228 + -6 Combine like terms: 7.348469228 + -6 = 1.348469228 q = 1.348469228 Simplifying q = 1.348469228

Subproblem 2

q + 6 = -7.348469228 Simplifying q + 6 = -7.348469228 Reorder the terms: 6 + q = -7.348469228 Solving 6 + q = -7.348469228 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + q = -7.348469228 + -6 Combine like terms: 6 + -6 = 0 0 + q = -7.348469228 + -6 q = -7.348469228 + -6 Combine like terms: -7.348469228 + -6 = -13.348469228 q = -13.348469228 Simplifying q = -13.348469228

Solution

The solution to the problem is based on the solutions from the subproblems. q = {1.348469228, -13.348469228}

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