If the quadratic formula is used to find the solution set of 3x2 + 4x - 2 = 0, what are the solutions?

Step-by-step explanation:

Compare to .

We have .

The quadratic formula is for solving equations of the form and is .

So we are going to plug in our values in that formula to find our solutions,x.

If you want to notice it in parts you can.

Example I might break it into these parts and then put it in:

Part 1: Evaluate

Part 2: Evaluate

Part 3: Evaluate

------Let's do these parts.

Part 1: .

This part 1 is important in determining the kinds of solutions you have. It is called the discriminant.  If it is positive, you have two real solutions.  If it is negative, you have no real solutions (both of the solutions are complex).  If it is 0, you have one real solution.

Part 2: since .

Part 3: .

Let's plug this in:

or in terms of our  parts:

40 itself is not a perfect square but it does contain a factor that is.  That factor is 4.

So we are going to rewrite 40 as .

I'm going to go ahead and separate the fraction like so:

Now I'm going to reduce both fractions:

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752