Question

How do you solve `3x^2-33=0`?

Answer 1

See a solution process below:

Explanation:

First, add `color(red)(33)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`3x^2 - 33 + color(red)(33) = 0 + color(red)(33)`

`3x^2 - 0 = 33`

`3x^2 = 33`

Next, divide each side of the equation by `color(red)(3)` to isolate the `x^2` while keeping the equation balanced:

`(3x^2)/color(red)(3) = 33/color(red)(3)`

`(color(red)(cancel(color(black)(3)))x^2)/cancel(color(red)(3)) = 11`

`x^2 = 11`

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(11)`

`x = +-sqrt(11)`

Or

`x = +-3.317` rounded to the nearest thousandth.