A^2-a+12=0 I need the roots

a = 1/2 (1 ±sqrt (47))

Step-by-step explanation:

a^2-a+12=0

We will complete the square

Subtract 12 from each side

a^2-a+12-12=0-12

a^2-a=-12

The coefficient of a = - 1

-Divide by 2 and then square it

(-1/2) ^2 = 1/4

Add it to each side

a^2 - a + 1/4=-12 + 1/4

(a-1/2) ^2 = - 11 3/4

(a-1/2) ^2 = - 47/4

Take the square root of each side

sqrt ((a-1/2) ^2) = sqrt (-47/4)

a-1/2 = ±i sqrt (1/4) sqrt (47)

a-1/2 = ±i/2 sqrt (47)

Add 1/2 to each side

a-1/2+1/2 = 1/2± i/2 sqrt (47)

a = 1/2± i/2 sqrt (47)

a = 1/2 (1 ±sqrt (47))