q^2+4q=16

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Solution for q^2+4q=16 equation:


Simplifying
q2 + 4q = 16

Reorder the terms:
4q + q2 = 16

Solving
4q + q2 = 16

Solving for variable 'q'.

Reorder the terms:
-16 + 4q + q2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 4q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 4q + 16 + q2 = 0 + 16

Reorder the terms:
-16 + 16 + 4q + q2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 4q + q2 = 0 + 16
4q + q2 = 0 + 16

Combine like terms: 0 + 16 = 16
4q + q2 = 16

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 = 16 + 4

Reorder the terms:
4 + 4q + q2 = 16 + 4

Combine like terms: 16 + 4 = 20
4 + 4q + q2 = 20

Factor a perfect square on the left side:
(q + 2)(q + 2) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(q + 2) equal to 4.472135955 and -4.472135955.

Subproblem 1

q + 2 = 4.472135955 Simplifying q + 2 = 4.472135955 Reorder the terms: 2 + q = 4.472135955 Solving 2 + q = 4.472135955 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 = 4.472135955 + -2 Combine like terms: 2 + -2 = 0 0 + q = 4.472135955 + -2 q = 4.472135955 + -2 Combine like terms: 4.472135955 + -2 = 2.472135955 q = 2.472135955 Simplifying q = 2.472135955

Subproblem 2

q + 2 = -4.472135955 Simplifying q + 2 = -4.472135955 Reorder the terms: 2 + q = -4.472135955 Solving 2 + q = -4.472135955 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 = -4.472135955 + -2 Combine like terms: 2 + -2 = 0 0 + q = -4.472135955 + -2 q = -4.472135955 + -2 Combine like terms: -4.472135955 + -2 = -6.472135955 q = -6.472135955 Simplifying q = -6.472135955

Solution

The solution to the problem is based on the solutions from the subproblems. q = {2.472135955, -6.472135955}

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