r^2=24+11r

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Solution for r^2=24+11r equation:


Simplifying
r2 = 24 + 11r

Solving
r2 = 24 + 11r

Solving for variable 'r'.

Reorder the terms:
-24 + -11r + r2 = 24 + 11r + -24 + -11r

Reorder the terms:
-24 + -11r + r2 = 24 + -24 + 11r + -11r

Combine like terms: 24 + -24 = 0
-24 + -11r + r2 = 0 + 11r + -11r
-24 + -11r + r2 = 11r + -11r

Combine like terms: 11r + -11r = 0
-24 + -11r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -11r + 24 + r2 = 0 + 24

Reorder the terms:
-24 + 24 + -11r + r2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -11r + r2 = 0 + 24
-11r + r2 = 0 + 24

Combine like terms: 0 + 24 = 24
-11r + r2 = 24

The r term is -11r.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11r + 30.25 + r2 = 24 + 30.25

Reorder the terms:
30.25 + -11r + r2 = 24 + 30.25

Combine like terms: 24 + 30.25 = 54.25
30.25 + -11r + r2 = 54.25

Factor a perfect square on the left side:
(r + -5.5)(r + -5.5) = 54.25

Calculate the square root of the right side: 7.365459931

Break this problem into two subproblems by setting 
(r + -5.5) equal to 7.365459931 and -7.365459931.

Subproblem 1

r + -5.5 = 7.365459931 Simplifying r + -5.5 = 7.365459931 Reorder the terms: -5.5 + r = 7.365459931 Solving -5.5 + r = 7.365459931 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + r = 7.365459931 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + r = 7.365459931 + 5.5 r = 7.365459931 + 5.5 Combine like terms: 7.365459931 + 5.5 = 12.865459931 r = 12.865459931 Simplifying r = 12.865459931

Subproblem 2

r + -5.5 = -7.365459931 Simplifying r + -5.5 = -7.365459931 Reorder the terms: -5.5 + r = -7.365459931 Solving -5.5 + r = -7.365459931 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + r = -7.365459931 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + r = -7.365459931 + 5.5 r = -7.365459931 + 5.5 Combine like terms: -7.365459931 + 5.5 = -1.865459931 r = -1.865459931 Simplifying r = -1.865459931

Solution

The solution to the problem is based on the solutions from the subproblems. r = {12.865459931, -1.865459931}

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