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

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


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

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

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

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

Solving for variable 'q'.

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

Combine like terms: q + 4q = 5q
-18 + 5q + 4q2 + -3q2 = 18 + -4q + 3q2 + -18 + 4q + -3q2

Combine like terms: 4q2 + -3q2 = 1q2
-18 + 5q + 1q2 = 18 + -4q + 3q2 + -18 + 4q + -3q2

Reorder the terms:
-18 + 5q + 1q2 = 18 + -18 + -4q + 4q + 3q2 + -3q2

Combine like terms: 18 + -18 = 0
-18 + 5q + 1q2 = 0 + -4q + 4q + 3q2 + -3q2
-18 + 5q + 1q2 = -4q + 4q + 3q2 + -3q2

Combine like terms: -4q + 4q = 0
-18 + 5q + 1q2 = 0 + 3q2 + -3q2
-18 + 5q + 1q2 = 3q2 + -3q2

Combine like terms: 3q2 + -3q2 = 0
-18 + 5q + 1q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 5q + 18 + q2 = 0 + 18

Reorder the terms:
-18 + 18 + 5q + q2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 5q + q2 = 0 + 18
5q + q2 = 0 + 18

Combine like terms: 0 + 18 = 18
5q + q2 = 18

The q term is 5q.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5q + 6.25 + q2 = 18 + 6.25

Reorder the terms:
6.25 + 5q + q2 = 18 + 6.25

Combine like terms: 18 + 6.25 = 24.25
6.25 + 5q + q2 = 24.25

Factor a perfect square on the left side:
(q + 2.5)(q + 2.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(q + 2.5) equal to 4.924428901 and -4.924428901.

Subproblem 1

q + 2.5 = 4.924428901 Simplifying q + 2.5 = 4.924428901 Reorder the terms: 2.5 + q = 4.924428901 Solving 2.5 + q = 4.924428901 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + q = 4.924428901 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + q = 4.924428901 + -2.5 q = 4.924428901 + -2.5 Combine like terms: 4.924428901 + -2.5 = 2.424428901 q = 2.424428901 Simplifying q = 2.424428901

Subproblem 2

q + 2.5 = -4.924428901 Simplifying q + 2.5 = -4.924428901 Reorder the terms: 2.5 + q = -4.924428901 Solving 2.5 + q = -4.924428901 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + q = -4.924428901 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + q = -4.924428901 + -2.5 q = -4.924428901 + -2.5 Combine like terms: -4.924428901 + -2.5 = -7.424428901 q = -7.424428901 Simplifying q = -7.424428901

Solution

The solution to the problem is based on the solutions from the subproblems. q = {2.424428901, -7.424428901}

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