r^2+24r=26

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Solution for r^2+24r=26 equation:


Simplifying
r2 + 24r = 26

Reorder the terms:
24r + r2 = 26

Solving
24r + r2 = 26

Solving for variable 'r'.

Reorder the terms:
-26 + 24r + r2 = 26 + -26

Combine like terms: 26 + -26 = 0
-26 + 24r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + 24r + 26 + r2 = 0 + 26

Reorder the terms:
-26 + 26 + 24r + r2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + 24r + r2 = 0 + 26
24r + r2 = 0 + 26

Combine like terms: 0 + 26 = 26
24r + r2 = 26

The r term is 24r.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24r + 144 + r2 = 26 + 144

Reorder the terms:
144 + 24r + r2 = 26 + 144

Combine like terms: 26 + 144 = 170
144 + 24r + r2 = 170

Factor a perfect square on the left side:
(r + 12)(r + 12) = 170

Calculate the square root of the right side: 13.03840481

Break this problem into two subproblems by setting 
(r + 12) equal to 13.03840481 and -13.03840481.

Subproblem 1

r + 12 = 13.03840481 Simplifying r + 12 = 13.03840481 Reorder the terms: 12 + r = 13.03840481 Solving 12 + r = 13.03840481 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + r = 13.03840481 + -12 Combine like terms: 12 + -12 = 0 0 + r = 13.03840481 + -12 r = 13.03840481 + -12 Combine like terms: 13.03840481 + -12 = 1.03840481 r = 1.03840481 Simplifying r = 1.03840481

Subproblem 2

r + 12 = -13.03840481 Simplifying r + 12 = -13.03840481 Reorder the terms: 12 + r = -13.03840481 Solving 12 + r = -13.03840481 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + r = -13.03840481 + -12 Combine like terms: 12 + -12 = 0 0 + r = -13.03840481 + -12 r = -13.03840481 + -12 Combine like terms: -13.03840481 + -12 = -25.03840481 r = -25.03840481 Simplifying r = -25.03840481

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.03840481, -25.03840481}

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