q^2+8q=27

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Solution for q^2+8q=27 equation:


Simplifying
q2 + 8q = 27

Reorder the terms:
8q + q2 = 27

Solving
8q + q2 = 27

Solving for variable 'q'.

Reorder the terms:
-27 + 8q + q2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + 8q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + 8q + 27 + q2 = 0 + 27

Reorder the terms:
-27 + 27 + 8q + q2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 8q + q2 = 0 + 27
8q + q2 = 0 + 27

Combine like terms: 0 + 27 = 27
8q + q2 = 27

The q term is 8q.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8q + 16 + q2 = 27 + 16

Reorder the terms:
16 + 8q + q2 = 27 + 16

Combine like terms: 27 + 16 = 43
16 + 8q + q2 = 43

Factor a perfect square on the left side:
(q + 4)(q + 4) = 43

Calculate the square root of the right side: 6.557438524

Break this problem into two subproblems by setting 
(q + 4) equal to 6.557438524 and -6.557438524.

Subproblem 1

q + 4 = 6.557438524 Simplifying q + 4 = 6.557438524 Reorder the terms: 4 + q = 6.557438524 Solving 4 + q = 6.557438524 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + q = 6.557438524 + -4 Combine like terms: 4 + -4 = 0 0 + q = 6.557438524 + -4 q = 6.557438524 + -4 Combine like terms: 6.557438524 + -4 = 2.557438524 q = 2.557438524 Simplifying q = 2.557438524

Subproblem 2

q + 4 = -6.557438524 Simplifying q + 4 = -6.557438524 Reorder the terms: 4 + q = -6.557438524 Solving 4 + q = -6.557438524 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + q = -6.557438524 + -4 Combine like terms: 4 + -4 = 0 0 + q = -6.557438524 + -4 q = -6.557438524 + -4 Combine like terms: -6.557438524 + -4 = -10.557438524 q = -10.557438524 Simplifying q = -10.557438524

Solution

The solution to the problem is based on the solutions from the subproblems. q = {2.557438524, -10.557438524}

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