q(q+4)=4

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Solution for q(q+4)=4 equation:


Simplifying
q(q + 4) = 4

Reorder the terms:
q(4 + q) = 4
(4 * q + q * q) = 4
(4q + q2) = 4

Solving
4q + q2 = 4

Solving for variable 'q'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 4 + 4

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

Combine like terms: 4 + 4 = 8
4 + 4q + q2 = 8

Factor a perfect square on the left side:
(q + 2)(q + 2) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(q + 2) equal to 2.828427125 and -2.828427125.

Subproblem 1

q + 2 = 2.828427125 Simplifying q + 2 = 2.828427125 Reorder the terms: 2 + q = 2.828427125 Solving 2 + q = 2.828427125 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 = 2.828427125 + -2 Combine like terms: 2 + -2 = 0 0 + q = 2.828427125 + -2 q = 2.828427125 + -2 Combine like terms: 2.828427125 + -2 = 0.828427125 q = 0.828427125 Simplifying q = 0.828427125

Subproblem 2

q + 2 = -2.828427125 Simplifying q + 2 = -2.828427125 Reorder the terms: 2 + q = -2.828427125 Solving 2 + q = -2.828427125 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 = -2.828427125 + -2 Combine like terms: 2 + -2 = 0 0 + q = -2.828427125 + -2 q = -2.828427125 + -2 Combine like terms: -2.828427125 + -2 = -4.828427125 q = -4.828427125 Simplifying q = -4.828427125

Solution

The solution to the problem is based on the solutions from the subproblems. q = {0.828427125, -4.828427125}

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