# In Desperate need of help: How do I go about solving 3^{x^2 + x} = 9.

#### mmm4444bot

##### Super Moderator
Staff member
Hint: Write 9 as 3^2

#### jedediahjamez

##### New member
Hint: Write 9 as 3^2
Thank you, but I’m still confused as to what to do with having 2 x variables. I’m sorry if I sound stupid but I’m a new student and I have a terrible teacher. Thanks again

#### mmm4444bot

##### Super Moderator
Staff member
Let's get a new equation, first. After subsituting 3^2 for 9, we have this:

3^(x^2 + x) = 3^2

This equation shows two powers of 3 set equal to one another. Can you use a basic property of exponents, to write another equation where x does not appear in any exponents?

#### jedediahjamez

##### New member
Let's get a new equation, first. After subsituting 3^2 for 9, we have this:

3^(x^2 + x) = 3^2

This equation shows two powers of 3 set equal to one another. Can you use a basic property of exponents, to write another equation where x does not appear in any exponents?
So the answer would be x=1 right? My school uses an online system to do homework and it’s telling me x=1 is wrong?

#### mmm4444bot

##### Super Moderator
Staff member
So the answer would be x=1 right?

Did you write (and maybe solve) a new equation, as I suggested? If so, may I see the equation and your work?

If you did not solve an equation, how did you get x = 1?

#### mmm4444bot

##### Super Moderator
Staff member
Here's the basic property of exponents that I have in mind:

Given b^m = b^n, then m = n

In other words, if two powers of the same base are equal, then the exponents must be equal. Here are some examples:

14^2 = 14^z means z = 2

A^(4y) = A^(y - 5) means 4y = y - 5

(3/4)^(t^3/17) = (3/4)^(4t^5) means t^3/17 = 4t^5

If you apply this property to the given equation in your exercise (after substituting 3^2 for 9), you'll get a basic quadratic equation to solve for x. (There are two solutions.)

#### stapel

##### Super Moderator
Staff member
So the answer would be x=1 right? My school uses an online system to do homework and it’s telling me x=1 is wrong?
Please reply showing how you followed through on the steps and hints you were provided. You created the equation they'd almost given you, you solved this using the Quadratic Formula, you got the two values, and... how did you get that "x=1" is the only answer?

$$\displaystyle x = 1 \implies x = 1 \implies x^2 = 1 \implies x^2 + x = 1 + 1 = 2 \implies 3^{(x^2 +x)} = 3^2.$$