r^2+5r+3=8

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Solution for r^2+5r+3=8 equation: 


Simplifying
r2 + 5r + 3 = 8

Reorder the terms:
3 + 5r + r2 = 8

Solving
3 + 5r + r2 = 8

Solving for variable 'r'.

Reorder the terms:
3 + -8 + 5r + r2 = 8 + -8

Combine like terms: 3 + -8 = -5
-5 + 5r + r2 = 8 + -8

Combine like terms: 8 + -8 = 0
-5 + 5r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 5r + 5 + r2 = 0 + 5

Reorder the terms:
-5 + 5 + 5r + r2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 5r + r2 = 0 + 5
5r + r2 = 0 + 5

Combine like terms: 0 + 5 = 5
5r + r2 = 5

The r term is 5r.  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.
5r + 6.25 + r2 = 5 + 6.25

Reorder the terms:
6.25 + 5r + r2 = 5 + 6.25

Combine like terms: 5 + 6.25 = 11.25
6.25 + 5r + r2 = 11.25

Factor a perfect square on the left side:
(r + 2.5)(r + 2.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(r + 2.5) equal to 3.354101966 and -3.354101966.


Subproblem 1
r + 2.5 = 3.354101966

Simplifying
r + 2.5 = 3.354101966

Reorder the terms:
2.5 + r = 3.354101966

Solving
2.5 + r = 3.354101966

Solving for variable 'r'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + r = 3.354101966 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + r = 3.354101966 + -2.5
r = 3.354101966 + -2.5

Combine like terms: 3.354101966 + -2.5 = 0.854101966
r = 0.854101966

Simplifying
r = 0.854101966


Subproblem 2
r + 2.5 = -3.354101966

Simplifying
r + 2.5 = -3.354101966

Reorder the terms:
2.5 + r = -3.354101966

Solving
2.5 + r = -3.354101966

Solving for variable 'r'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + r = -3.354101966 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + r = -3.354101966 + -2.5
r = -3.354101966 + -2.5

Combine like terms: -3.354101966 + -2.5 = -5.854101966
r = -5.854101966

Simplifying
r = -5.854101966


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.854101966, -5.854101966}

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