r^2=11r-24

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


Simplifying
r2 = 11r + -24

Reorder the terms:
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

Factor a trinomial.
(3 + -1r)(8 + -1r) = 0

Subproblem 1

Set the factor '(3 + -1r)' equal to zero and attempt to solve: Simplifying 3 + -1r = 0 Solving 3 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1r = 0 + -3 -1r = 0 + -3 Combine like terms: 0 + -3 = -3 -1r = -3 Divide each side by '-1'. r = 3 Simplifying r = 3

Subproblem 2

Set the factor '(8 + -1r)' equal to zero and attempt to solve: Simplifying 8 + -1r = 0 Solving 8 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1r = 0 + -8 -1r = 0 + -8 Combine like terms: 0 + -8 = -8 -1r = -8 Divide each side by '-1'. r = 8 Simplifying r = 8

Solution

r = {3, 8}

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