r^2-4r-5=-3

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Solution for r^2-4r-5=-3 equation: 


Simplifying
r2 + -4r + -5 = -3

Reorder the terms:
-5 + -4r + r2 = -3

Solving
-5 + -4r + r2 = -3

Solving for variable 'r'.

Reorder the terms:
-5 + 3 + -4r + r2 = -3 + 3

Combine like terms: -5 + 3 = -2
-2 + -4r + r2 = -3 + 3

Combine like terms: -3 + 3 = 0
-2 + -4r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -4r + 2 + r2 = 0 + 2

Reorder the terms:
-2 + 2 + -4r + r2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -4r + r2 = 0 + 2
-4r + r2 = 0 + 2

Combine like terms: 0 + 2 = 2
-4r + r2 = 2

The r term is -4r.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4r + 4 + r2 = 2 + 4

Reorder the terms:
4 + -4r + r2 = 2 + 4

Combine like terms: 2 + 4 = 6
4 + -4r + r2 = 6

Factor a perfect square on the left side:
(r + -2)(r + -2) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(r + -2) equal to 2.449489743 and -2.449489743.


Subproblem 1
r + -2 = 2.449489743

Simplifying
r + -2 = 2.449489743

Reorder the terms:
-2 + r = 2.449489743

Solving
-2 + r = 2.449489743

Solving for variable 'r'.

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

Add '2' to each side of the equation.
-2 + 2 + r = 2.449489743 + 2

Combine like terms: -2 + 2 = 0
0 + r = 2.449489743 + 2
r = 2.449489743 + 2

Combine like terms: 2.449489743 + 2 = 4.449489743
r = 4.449489743

Simplifying
r = 4.449489743


Subproblem 2
r + -2 = -2.449489743

Simplifying
r + -2 = -2.449489743

Reorder the terms:
-2 + r = -2.449489743

Solving
-2 + r = -2.449489743

Solving for variable 'r'.

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

Add '2' to each side of the equation.
-2 + 2 + r = -2.449489743 + 2

Combine like terms: -2 + 2 = 0
0 + r = -2.449489743 + 2
r = -2.449489743 + 2

Combine like terms: -2.449489743 + 2 = -0.449489743
r = -0.449489743

Simplifying
r = -0.449489743


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.449489743, -0.449489743}

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