48r=9+r^2

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Solution for 48r=9+r^2 equation:


Simplifying
48r = 9 + r2

Solving
48r = 9 + r2

Solving for variable 'r'.

Reorder the terms:
-9 + 48r + -1r2 = 9 + r2 + -9 + -1r2

Reorder the terms:
-9 + 48r + -1r2 = 9 + -9 + r2 + -1r2

Combine like terms: 9 + -9 = 0
-9 + 48r + -1r2 = 0 + r2 + -1r2
-9 + 48r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
-9 + 48r + -1r2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
9 + -48r + r2 = 0

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -48r + -9 + r2 = 0 + -9

Reorder the terms:
9 + -9 + -48r + r2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -48r + r2 = 0 + -9
-48r + r2 = 0 + -9

Combine like terms: 0 + -9 = -9
-48r + r2 = -9

The r term is -48r.  Take half its coefficient (-24).
Square it (576) and add it to both sides.

Add '576' to each side of the equation.
-48r + 576 + r2 = -9 + 576

Reorder the terms:
576 + -48r + r2 = -9 + 576

Combine like terms: -9 + 576 = 567
576 + -48r + r2 = 567

Factor a perfect square on the left side:
(r + -24)(r + -24) = 567

Calculate the square root of the right side: 23.8117618

Break this problem into two subproblems by setting 
(r + -24) equal to 23.8117618 and -23.8117618.

Subproblem 1

r + -24 = 23.8117618 Simplifying r + -24 = 23.8117618 Reorder the terms: -24 + r = 23.8117618 Solving -24 + r = 23.8117618 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + r = 23.8117618 + 24 Combine like terms: -24 + 24 = 0 0 + r = 23.8117618 + 24 r = 23.8117618 + 24 Combine like terms: 23.8117618 + 24 = 47.8117618 r = 47.8117618 Simplifying r = 47.8117618

Subproblem 2

r + -24 = -23.8117618 Simplifying r + -24 = -23.8117618 Reorder the terms: -24 + r = -23.8117618 Solving -24 + r = -23.8117618 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + r = -23.8117618 + 24 Combine like terms: -24 + 24 = 0 0 + r = -23.8117618 + 24 r = -23.8117618 + 24 Combine like terms: -23.8117618 + 24 = 0.1882382 r = 0.1882382 Simplifying r = 0.1882382

Solution

The solution to the problem is based on the solutions from the subproblems. r = {47.8117618, 0.1882382}

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