Question

How do you solve this? r^2+32=12r

Answer 1

Answer:

r = {-8, -4}

Step-by-step explanation:

Simplifying

r2 = -32 + -12r

Solving

r2 = -32 + -12r

Solving for variable 'r'.

Reorder the terms:

32 + 12r + r2 = -32 + -12r + 32 + 12r

Reorder the terms:

32 + 12r + r2 = -32 + 32 + -12r + 12r

Combine like terms: -32 + 32 = 0

32 + 12r + r2 = 0 + -12r + 12r

32 + 12r + r2 = -12r + 12r

Combine like terms: -12r + 12r = 0

32 + 12r + r2 = 0

Factor a trinomial.

(8 + r)(4 + r) = 0

Subproblem 1

Set the factor '(8 + r)' equal to zero and attempt to solve:

Simplifying

8 + r = 0

Solving

8 + r = 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 + r = 0 + -8

Combine like terms: 8 + -8 = 0

0 + r = 0 + -8

r = 0 + -8

Combine like terms: 0 + -8 = -8

r = -8

Simplifying

r = -8

Subproblem 2

Set the factor '(4 + r)' equal to zero and attempt to solve:

Simplifying

4 + r = 0

Solving

4 + r = 0

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

Add '-4' to each side of the equation.

4 + -4 + r = 0 + -4

Combine like terms: 4 + -4 = 0

0 + r = 0 + -4

r = 0 + -4

Combine like terms: 0 + -4 = -4

r = -4

Simplifying

r = -4

Solution

r = {-8, -4}