q*q+5*q-3=16

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Solution for q*q+5*q-3=16 equation: 


Simplifying
q * q + 5q + -3 = 16

Multiply q * q
q2 + 5q + -3 = 16

Reorder the terms:
-3 + 5q + q2 = 16

Solving
-3 + 5q + q2 = 16

Solving for variable 'q'.

Reorder the terms:
-3 + -16 + 5q + q2 = 16 + -16

Combine like terms: -3 + -16 = -19
-19 + 5q + q2 = 16 + -16

Combine like terms: 16 + -16 = 0
-19 + 5q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + 5q + 19 + q2 = 0 + 19

Reorder the terms:
-19 + 19 + 5q + q2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 5q + q2 = 0 + 19
5q + q2 = 0 + 19

Combine like terms: 0 + 19 = 19
5q + q2 = 19

The q term is 5q.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5q + 6.25 + q2 = 19 + 6.25

Reorder the terms:
6.25 + 5q + q2 = 19 + 6.25

Combine like terms: 19 + 6.25 = 25.25
6.25 + 5q + q2 = 25.25

Factor a perfect square on the left side:
(q + 2.5)(q + 2.5) = 25.25

Calculate the square root of the right side: 5.024937811

Break this problem into two subproblems by setting 
(q + 2.5) equal to 5.024937811 and -5.024937811.


Subproblem 1
q + 2.5 = 5.024937811

Simplifying
q + 2.5 = 5.024937811

Reorder the terms:
2.5 + q = 5.024937811

Solving
2.5 + q = 5.024937811

Solving for variable 'q'.

Move all terms containing q to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + q = 5.024937811 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + q = 5.024937811 + -2.5
q = 5.024937811 + -2.5

Combine like terms: 5.024937811 + -2.5 = 2.524937811
q = 2.524937811

Simplifying
q = 2.524937811


Subproblem 2
q + 2.5 = -5.024937811

Simplifying
q + 2.5 = -5.024937811

Reorder the terms:
2.5 + q = -5.024937811

Solving
2.5 + q = -5.024937811

Solving for variable 'q'.

Move all terms containing q to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + q = -5.024937811 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + q = -5.024937811 + -2.5
q = -5.024937811 + -2.5

Combine like terms: -5.024937811 + -2.5 = -7.524937811
q = -7.524937811

Simplifying
q = -7.524937811


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {2.524937811, -7.524937811}

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