# Find all solutions to the equation sqrt(2-3x)= 9. Express your answer as a common fraction.

I squared both sides and I got 4-9z^2=81 and then -9z^2=77 then I divided both sides by -9 and now I am stuck, I know I can square root both sides. But I think something went wrong.

## √(2-3x) = 9

2-3x = 81
3x = -79
x = -79/3

Remember: (a-bx)^2 is NOT NOT a^2 - b^2x^2

Not that that matters here, anyway, since

√(stuff)^2 is just stuff, whatever stuff you have.

(√x)^2 = √(x^2) = x. There is no reason at all to square what's inside the radical. It just emerges unchanged when the square toot is squared.

## Well, let's go through the steps again and see if we can figure out what went wrong.

Starting with sqrt(2-3x) = 9, if we square both sides, we get (2-3x) = 81. So far, so good!

Next, let's simplify the equation by subtracting 2 from both sides: -3x = 79.

Now, let's be careful and divide both sides by -3. This gives us x = -79/3.

So, the solution to the equation sqrt(2-3x) = 9 is x = -79/3.

Remember, it's always a good idea to double-check your work to avoid any scary math circus accidents!

## Let's go step by step to solve the equation sqrt(2-3x)=9:

1. Start by isolating the square root term. Square both sides of the equation to get rid of the square root:

(sqrt(2-3x))^2 = 9^2
2-3x = 81

2. Now, we have the equation 2-3x = 81. To solve for x, isolate the variable term:

-3x = 81-2
-3x = 79

3. Divide both sides of the equation by -3 to solve for x:

x = 79/-3
x = -79/3

Therefore, the solution to the equation sqrt(2-3x)=9 is x = -79/3.

## To solve the equation sqrt(2-3x) = 9, you started by squaring both sides of the equation. However, when squaring a square root, it is important to include both the positive and negative solutions. So, the correct equation would be:

2-3x = 81

Now, let's solve for x:

First, subtract 2 from both sides of the equation:

-3x = 81 - 2

-3x = 79

Next, divide both sides by -3 to isolate x:

x = 79/-3

This simplifies to:

x = -79/3

So, the solution to the equation sqrt(2-3x) = 9 is x = -79/3.