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.

m = .43, 11.57

Step-by-step 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

6 - √31

6 + √31

Step-by-step explanation:

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.