Question

Solve by completing the square.

m2 − 12m + 5 = 0

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

Answer 1

6 - √31

6 + √31

Explanation:

• m² − 12m + 5 = 0
• m² − 2*6m + 36-31 = 0
• (m-6)²-31=0
• (m-6+√31)(m-6-√31)=0
• m-6+√31=0 ⇒ m= 6-√31
• m-6-√31=0 ⇒ m=6+√31

Answer 2

m = .43, 11.57

Explanation:

m^2 − 12m + 5 = 0

Subtract 5 from each side

m^2 − 12m + 5 -5= 0-5

m^2 − 12m = -5

Take the coefficient of m

-12

Divide by 2

-12/2 = -6

Square it

(-6)^2 = 36

Add it to each side

m^2 − 12m +36= -5+36

(m -6)^2=31

Take the square root of each side

sqrt(m -6)^2=±sqrt(31)

m-6 = ±sqrt(31)

Add 6 to each side

m-6+6 = 6±sqrt(31)

m = 6±sqrt(31)

m = 6+sqrt(31)=11.56776

= 6 - sqrt(31)=0.43223

Rounding to the nearest hundredth

m = .43, 11.57