3r^2-78r+87=0

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Solution for 3r^2-78r+87=0 equation: 


Simplifying
3r2 + -78r + 87 = 0

Reorder the terms:
87 + -78r + 3r2 = 0

Solving
87 + -78r + 3r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(29 + -26r + r2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(29 + -26r + r2)' equal to zero and attempt to solve:

Simplifying
29 + -26r + r2 = 0

Solving
29 + -26r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-29' to each side of the equation.
29 + -26r + -29 + r2 = 0 + -29

Reorder the terms:
29 + -29 + -26r + r2 = 0 + -29

Combine like terms: 29 + -29 = 0
0 + -26r + r2 = 0 + -29
-26r + r2 = 0 + -29

Combine like terms: 0 + -29 = -29
-26r + r2 = -29

The r term is -26r.  Take half its coefficient (-13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
-26r + 169 + r2 = -29 + 169

Reorder the terms:
169 + -26r + r2 = -29 + 169

Combine like terms: -29 + 169 = 140
169 + -26r + r2 = 140

Factor a perfect square on the left side:
(r + -13)(r + -13) = 140

Calculate the square root of the right side: 11.832159566

Break this problem into two subproblems by setting 
(r + -13) equal to 11.832159566 and -11.832159566.


Subproblem 1
r + -13 = 11.832159566

Simplifying
r + -13 = 11.832159566

Reorder the terms:
-13 + r = 11.832159566

Solving
-13 + r = 11.832159566

Solving for variable 'r'.

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

Add '13' to each side of the equation.
-13 + 13 + r = 11.832159566 + 13

Combine like terms: -13 + 13 = 0
0 + r = 11.832159566 + 13
r = 11.832159566 + 13

Combine like terms: 11.832159566 + 13 = 24.832159566
r = 24.832159566

Simplifying
r = 24.832159566


Subproblem 2
r + -13 = -11.832159566

Simplifying
r + -13 = -11.832159566

Reorder the terms:
-13 + r = -11.832159566

Solving
-13 + r = -11.832159566

Solving for variable 'r'.

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

Add '13' to each side of the equation.
-13 + 13 + r = -11.832159566 + 13

Combine like terms: -13 + 13 = 0
0 + r = -11.832159566 + 13
r = -11.832159566 + 13

Combine like terms: -11.832159566 + 13 = 1.167840434
r = 1.167840434

Simplifying
r = 1.167840434


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {24.832159566, 1.167840434}
Solution
r = {24.832159566, 1.167840434}

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