Question

How do you find the zeros of `x^2= 30-13x`?

Answer 1

First, get all of the terms for the quadratic on the left side of the equation, factor the quadratic and then solve each term for `0`. See full explanation below.

Explanation:

First, get all terms on the left side of the equation while keeping the equation balanced:

`x^2 + color(red)(13x) - color(blue)(30) = 30 - 13x + color(red)(13x) - color(blue)(30)`

`x^2 + color(red)(13x) - color(blue)(30) = 30 - color(blue)(30) - 13x + color(red)(13x)`

`x^2 + color(red)(13x) - color(blue)(30) = 0 - 0`

`x^2 + color(red)(13x) - color(blue)(30) = 0`

We can now factor the quadratic:

`(x + 15)(x - 2) = 0`

Finally we can solve each term for `0`:

Solution 1)

`x + 15 = 0`

`x + 15 - color(red)(15) = 0 - color(red)(15)`

`x + 0 = -15`

`x = -15`

Solution 2)

`x - 2 = 0`

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

`x - 0 = 2`

`x = 2`