q^2+16q=23

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Solution for q^2+16q=23 equation:


Simplifying
q2 + 16q = 23

Reorder the terms:
16q + q2 = 23

Solving
16q + q2 = 23

Solving for variable 'q'.

Reorder the terms:
-23 + 16q + q2 = 23 + -23

Combine like terms: 23 + -23 = 0
-23 + 16q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + 16q + 23 + q2 = 0 + 23

Reorder the terms:
-23 + 23 + 16q + q2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + 16q + q2 = 0 + 23
16q + q2 = 0 + 23

Combine like terms: 0 + 23 = 23
16q + q2 = 23

The q term is 16q.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16q + 64 + q2 = 23 + 64

Reorder the terms:
64 + 16q + q2 = 23 + 64

Combine like terms: 23 + 64 = 87
64 + 16q + q2 = 87

Factor a perfect square on the left side:
(q + 8)(q + 8) = 87

Calculate the square root of the right side: 9.327379053

Break this problem into two subproblems by setting 
(q + 8) equal to 9.327379053 and -9.327379053.

Subproblem 1

q + 8 = 9.327379053 Simplifying q + 8 = 9.327379053 Reorder the terms: 8 + q = 9.327379053 Solving 8 + q = 9.327379053 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + q = 9.327379053 + -8 Combine like terms: 8 + -8 = 0 0 + q = 9.327379053 + -8 q = 9.327379053 + -8 Combine like terms: 9.327379053 + -8 = 1.327379053 q = 1.327379053 Simplifying q = 1.327379053

Subproblem 2

q + 8 = -9.327379053 Simplifying q + 8 = -9.327379053 Reorder the terms: 8 + q = -9.327379053 Solving 8 + q = -9.327379053 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + q = -9.327379053 + -8 Combine like terms: 8 + -8 = 0 0 + q = -9.327379053 + -8 q = -9.327379053 + -8 Combine like terms: -9.327379053 + -8 = -17.327379053 q = -17.327379053 Simplifying q = -17.327379053

Solution

The solution to the problem is based on the solutions from the subproblems. q = {1.327379053, -17.327379053}

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