q^2+10q-16=0

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Solution for q^2+10q-16=0 equation: 


Simplifying
q2 + 10q + -16 = 0

Reorder the terms:
-16 + 10q + q2 = 0

Solving
-16 + 10q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 10q + 16 + q2 = 0 + 16

Reorder the terms:
-16 + 16 + 10q + q2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 10q + q2 = 0 + 16
10q + q2 = 0 + 16

Combine like terms: 0 + 16 = 16
10q + q2 = 16

The q term is 10q.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10q + 25 + q2 = 16 + 25

Reorder the terms:
25 + 10q + q2 = 16 + 25

Combine like terms: 16 + 25 = 41
25 + 10q + q2 = 41

Factor a perfect square on the left side:
(q + 5)(q + 5) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(q + 5) equal to 6.403124237 and -6.403124237.


Subproblem 1
q + 5 = 6.403124237

Simplifying
q + 5 = 6.403124237

Reorder the terms:
5 + q = 6.403124237

Solving
5 + q = 6.403124237

Solving for variable 'q'.

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

Add '-5' to each side of the equation.
5 + -5 + q = 6.403124237 + -5

Combine like terms: 5 + -5 = 0
0 + q = 6.403124237 + -5
q = 6.403124237 + -5

Combine like terms: 6.403124237 + -5 = 1.403124237
q = 1.403124237

Simplifying
q = 1.403124237


Subproblem 2
q + 5 = -6.403124237

Simplifying
q + 5 = -6.403124237

Reorder the terms:
5 + q = -6.403124237

Solving
5 + q = -6.403124237

Solving for variable 'q'.

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

Add '-5' to each side of the equation.
5 + -5 + q = -6.403124237 + -5

Combine like terms: 5 + -5 = 0
0 + q = -6.403124237 + -5
q = -6.403124237 + -5

Combine like terms: -6.403124237 + -5 = -11.403124237
q = -11.403124237

Simplifying
q = -11.403124237


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {1.403124237, -11.403124237}

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