# How to Solve the Equation y^2+z^2=1 - Comprehensive Guide

Are you trying to find the exact solutions to the equation `y^2+z^2=1`? Solving this type of equation can be tricky but it is very doable. In this guide, we will walk through step-by-step the process of solving this equation.

## Isolate the Variable

The first step to solving the equation is to isolate the variable we want to solve for. In this case, we want to solve for `z` so move it all to one side.

We start by subtracting `y^2` from both sides of the equation, isolating `z^2`:

`y^2+z^2 = 1`
`-y^2`      `-y^2`

`z^2 = 1 - y^2`

## Taking the Square Root of Both Sides

Now, we will take the square root of both sides of our equation, giving us two solutions.

`&radic;(z^2) = &radic;(1-y^2)`

We can now rewrite our equation as:

`z = &plusmn;&radic;(1-y^2)`

## Find the Solutions

This gives us two solutions, one positive and one negative.

`z = &radic;(1-y^2)`

`z = -&radic;(1-y^2)`

## FAQ

### What are the solutions of the equation y^2+z^2=1?

The solutions of the equation `y^2+z^2=1` are `z = &radic;(1-y^2)` and `z = -&radic;(1-y^2)`.

### Does solving the equation y^2+z^2=1 require any special techniques?

Yes, in order to solve the equation `y^2+z^2=1`, you will need to use the technique of isolating the variable as well as taking the square root of both sides of the equation.

### What should I do if I'm having trouble solving the equation y^2+z^2=1?

If you're having trouble solving the equation `y^2+z^2=1`, make sure to carefully go through each step and understand the technique required to solve the equation. You may also want to get help from a tutor if needed.

### What type of equation is y^2+z^2=1?

The equation `y^2+z^2=1` is a quadratic equation.

### How do I know when I have solved the equation y^2+z^2=1 correctly?

You will know you have solved the equation `y^2+z^2=1` correctly when your answer is in the form of z = ±√(1-y^^2).

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