r^2-16r-75=-10

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Solution for r^2-16r-75=-10 equation:


Simplifying
r2 + -16r + -75 = -10

Reorder the terms:
-75 + -16r + r2 = -10

Solving
-75 + -16r + r2 = -10

Solving for variable 'r'.

Reorder the terms:
-75 + 10 + -16r + r2 = -10 + 10

Combine like terms: -75 + 10 = -65
-65 + -16r + r2 = -10 + 10

Combine like terms: -10 + 10 = 0
-65 + -16r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '65' to each side of the equation.
-65 + -16r + 65 + r2 = 0 + 65

Reorder the terms:
-65 + 65 + -16r + r2 = 0 + 65

Combine like terms: -65 + 65 = 0
0 + -16r + r2 = 0 + 65
-16r + r2 = 0 + 65

Combine like terms: 0 + 65 = 65
-16r + r2 = 65

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

Add '64' to each side of the equation.
-16r + 64 + r2 = 65 + 64

Reorder the terms:
64 + -16r + r2 = 65 + 64

Combine like terms: 65 + 64 = 129
64 + -16r + r2 = 129

Factor a perfect square on the left side:
(r + -8)(r + -8) = 129

Calculate the square root of the right side: 11.357816692

Break this problem into two subproblems by setting 
(r + -8) equal to 11.357816692 and -11.357816692.


Subproblem 1
r + -8 = 11.357816692

Simplifying
r + -8 = 11.357816692

Reorder the terms:
-8 + r = 11.357816692

Solving
-8 + r = 11.357816692

Solving for variable 'r'.

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

Add '8' to each side of the equation.
-8 + 8 + r = 11.357816692 + 8

Combine like terms: -8 + 8 = 0
0 + r = 11.357816692 + 8
r = 11.357816692 + 8

Combine like terms: 11.357816692 + 8 = 19.357816692
r = 19.357816692

Simplifying
r = 19.357816692


Subproblem 2
r + -8 = -11.357816692

Simplifying
r + -8 = -11.357816692

Reorder the terms:
-8 + r = -11.357816692

Solving
-8 + r = -11.357816692

Solving for variable 'r'.

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

Add '8' to each side of the equation.
-8 + 8 + r = -11.357816692 + 8

Combine like terms: -8 + 8 = 0
0 + r = -11.357816692 + 8
r = -11.357816692 + 8

Combine like terms: -11.357816692 + 8 = -3.357816692
r = -3.357816692

Simplifying
r = -3.357816692


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {19.357816692, -3.357816692}

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