Question

How do you solve the equation `x^2-19=0`?

Answer 1

See the solution process below:

Explanation:

First, add `color(red)(19)` to each side of the equation to isolate the `x^2` term while keeping the equation balanced:

`x^2 - 19 + color(red)(19) = 0 + color(red)(19)`

`x^2 - 0 = 19`

`x^2 = 19`

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

`sqrt(x^2) = sqrt(19)`

`x = +-4.359` rounded to the nearest thousandth.