10r^2-2r-16=2

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Solution for 10r^2-2r-16=2 equation: 


Simplifying
10r2 + -2r + -16 = 2

Reorder the terms:
-16 + -2r + 10r2 = 2

Solving
-16 + -2r + 10r2 = 2

Solving for variable 'r'.

Reorder the terms:
-16 + -2 + -2r + 10r2 = 2 + -2

Combine like terms: -16 + -2 = -18
-18 + -2r + 10r2 = 2 + -2

Combine like terms: 2 + -2 = 0
-18 + -2r + 10r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -1r + 5r2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + -1r + 5r2)' equal to zero and attempt to solve:

Simplifying
-9 + -1r + 5r2 = 0

Solving
-9 + -1r + 5r2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-1.8 + -0.2r + r2 = 0

Move the constant term to the right:

Add '1.8' to each side of the equation.
-1.8 + -0.2r + 1.8 + r2 = 0 + 1.8

Reorder the terms:
-1.8 + 1.8 + -0.2r + r2 = 0 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + -0.2r + r2 = 0 + 1.8
-0.2r + r2 = 0 + 1.8

Combine like terms: 0 + 1.8 = 1.8
-0.2r + r2 = 1.8

The r term is -0.2r.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2r + 0.01 + r2 = 1.8 + 0.01

Reorder the terms:
0.01 + -0.2r + r2 = 1.8 + 0.01

Combine like terms: 1.8 + 0.01 = 1.81
0.01 + -0.2r + r2 = 1.81

Factor a perfect square on the left side:
(r + -0.1)(r + -0.1) = 1.81

Calculate the square root of the right side: 1.345362405

Break this problem into two subproblems by setting 
(r + -0.1) equal to 1.345362405 and -1.345362405.


Subproblem 1
r + -0.1 = 1.345362405

Simplifying
r + -0.1 = 1.345362405

Reorder the terms:
-0.1 + r = 1.345362405

Solving
-0.1 + r = 1.345362405

Solving for variable 'r'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + r = 1.345362405 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + r = 1.345362405 + 0.1
r = 1.345362405 + 0.1

Combine like terms: 1.345362405 + 0.1 = 1.445362405
r = 1.445362405

Simplifying
r = 1.445362405


Subproblem 2
r + -0.1 = -1.345362405

Simplifying
r + -0.1 = -1.345362405

Reorder the terms:
-0.1 + r = -1.345362405

Solving
-0.1 + r = -1.345362405

Solving for variable 'r'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + r = -1.345362405 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + r = -1.345362405 + 0.1
r = -1.345362405 + 0.1

Combine like terms: -1.345362405 + 0.1 = -1.245362405
r = -1.245362405

Simplifying
r = -1.245362405


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.445362405, -1.245362405}
Solution
r = {1.445362405, -1.245362405}

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