square root of 3a^2-32=a

Question

simple radical equations

Answer 1

√(3a²-32)=a

square both sides

3a²-32=a²

3a²-a²-32=0

2a²-32=0

a²-16=0

(a-4)(a+4)=0

a-4=0

a=4

a+4=0

a=-4 but the symbol  √ denotes the principal or nonnegative  root

Answer 2

The equation to be solved is 3a^2 - a -32 =0, the solution for the quadratic is x = (-b±√(b^2-4ac))/2a, we have  then that a= 3, b=-1, c=-32. Plugging this numbers in we have:

x1 or a1 = (1 + √(1 + 4*3*32))/2*3 = (1+√(385))/6 = (1+19.62)/6 =3.44;

and a2 will be (1-19.62)/6 = 3.1