Solve: (2a²+5a+2) ^1/2=3

When you have an expression to the power of (1/2) that means the same thing as having a square root.

Lets call a=x

To get rid of the square root we square both sides getting:

2x^2+5x+2 = 3^2

Simplifying this we get: 2x^2+5x+2=9

We can subtract 9 from both sides getting: 2x^2+5x-7

Now when we solve for this we can use the quadratic formula:

(-b + / - sqrt (b^2-4ac)) / 2a

a=2, b=5, c=-7

Plugging in we end up with : (-5 + / - sqrt (81)) / 4

This simplifies to : (-5 + / - 9) / 4 ... (-5 + (-9)) / 4 OR (-5 - (-9)) / 4

we have x = - 14/4, 1

Answer: a = - 7/2 or a = 1