r(r-18.7)=19.7

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Solution for r(r-18.7)=19.7 equation: 


Simplifying
r(r + -18.7) = 19.7

Reorder the terms:
r(-18.7 + r) = 19.7
(-18.7 * r + r * r) = 19.7
(-18.7r + r2) = 19.7

Solving
-18.7r + r2 = 19.7

Solving for variable 'r'.

Reorder the terms:
-19.7 + -18.7r + r2 = 19.7 + -19.7

Combine like terms: 19.7 + -19.7 = 0.0
-19.7 + -18.7r + r2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '19.7' to each side of the equation.
-19.7 + -18.7r + 19.7 + r2 = 0.0 + 19.7

Reorder the terms:
-19.7 + 19.7 + -18.7r + r2 = 0.0 + 19.7

Combine like terms: -19.7 + 19.7 = 0.0
0.0 + -18.7r + r2 = 0.0 + 19.7
-18.7r + r2 = 0.0 + 19.7

Combine like terms: 0.0 + 19.7 = 19.7
-18.7r + r2 = 19.7

The r term is -18.7r.  Take half its coefficient (-9.35).
Square it (87.4225) and add it to both sides.

Add '87.4225' to each side of the equation.
-18.7r + 87.4225 + r2 = 19.7 + 87.4225

Reorder the terms:
87.4225 + -18.7r + r2 = 19.7 + 87.4225

Combine like terms: 19.7 + 87.4225 = 107.1225
87.4225 + -18.7r + r2 = 107.1225

Factor a perfect square on the left side:
(r + -9.35)(r + -9.35) = 107.1225

Calculate the square root of the right side: 10.35

Break this problem into two subproblems by setting 
(r + -9.35) equal to 10.35 and -10.35.


Subproblem 1
r + -9.35 = 10.35

Simplifying
r + -9.35 = 10.35

Reorder the terms:
-9.35 + r = 10.35

Solving
-9.35 + r = 10.35

Solving for variable 'r'.

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

Add '9.35' to each side of the equation.
-9.35 + 9.35 + r = 10.35 + 9.35

Combine like terms: -9.35 + 9.35 = 0.00
0.00 + r = 10.35 + 9.35
r = 10.35 + 9.35

Combine like terms: 10.35 + 9.35 = 19.7
r = 19.7

Simplifying
r = 19.7


Subproblem 2
r + -9.35 = -10.35

Simplifying
r + -9.35 = -10.35

Reorder the terms:
-9.35 + r = -10.35

Solving
-9.35 + r = -10.35

Solving for variable 'r'.

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

Add '9.35' to each side of the equation.
-9.35 + 9.35 + r = -10.35 + 9.35

Combine like terms: -9.35 + 9.35 = 0.00
0.00 + r = -10.35 + 9.35
r = -10.35 + 9.35

Combine like terms: -10.35 + 9.35 = -1
r = -1

Simplifying
r = -1


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {19.7, -1}

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