q^2+4q=49

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Solution for q^2+4q=49 equation:


Simplifying
q2 + 4q = 49

Reorder the terms:
4q + q2 = 49

Solving
4q + q2 = 49

Solving for variable 'q'.

Reorder the terms:
-49 + 4q + q2 = 49 + -49

Combine like terms: 49 + -49 = 0
-49 + 4q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + 4q + 49 + q2 = 0 + 49

Reorder the terms:
-49 + 49 + 4q + q2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + 4q + q2 = 0 + 49
4q + q2 = 0 + 49

Combine like terms: 0 + 49 = 49
4q + q2 = 49

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 = 49 + 4

Reorder the terms:
4 + 4q + q2 = 49 + 4

Combine like terms: 49 + 4 = 53
4 + 4q + q2 = 53

Factor a perfect square on the left side:
(q + 2)(q + 2) = 53

Calculate the square root of the right side: 7.280109889

Break this problem into two subproblems by setting 
(q + 2) equal to 7.280109889 and -7.280109889.

Subproblem 1

q + 2 = 7.280109889 Simplifying q + 2 = 7.280109889 Reorder the terms: 2 + q = 7.280109889 Solving 2 + q = 7.280109889 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 = 7.280109889 + -2 Combine like terms: 2 + -2 = 0 0 + q = 7.280109889 + -2 q = 7.280109889 + -2 Combine like terms: 7.280109889 + -2 = 5.280109889 q = 5.280109889 Simplifying q = 5.280109889

Subproblem 2

q + 2 = -7.280109889 Simplifying q + 2 = -7.280109889 Reorder the terms: 2 + q = -7.280109889 Solving 2 + q = -7.280109889 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 = -7.280109889 + -2 Combine like terms: 2 + -2 = 0 0 + q = -7.280109889 + -2 q = -7.280109889 + -2 Combine like terms: -7.280109889 + -2 = -9.280109889 q = -9.280109889 Simplifying q = -9.280109889

Solution

The solution to the problem is based on the solutions from the subproblems. q = {5.280109889, -9.280109889}

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