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.