Question

How do you solve `13p^2-3=4209`?

Answer 1

See the entire solution process below:

Explanation:

First, add `color(red)(3)` to each side of the equation to isolate the `p` term while keeping the equation balanced:

`13p^2 - 3 + color(red)(3) = 4209 + color(red)(3)`

`13p^2 - 0 = 4212`

`13p^2 = 4212`

Now, divide each side of the equation by `color(red)(13)` to isolate `p^2` while keeping the equation balanced:

`(13p^2)/color(red)(13) = 4212/color(red)(13)`

`(color(red)(cancel(color(black)(13)))p^2)/cancel(color(red)(13)) = 324`

`p^2 = 324`

Now, take the square root of each side of the equation to solve for `p`. Remember, the square root of a number produces a negative and positive result:

`sqrt(p^2) = +-sqrt(324)`

`p = +-18`