Question

How do you solve `\frac { 1} { 3} x ^ { 2} + 2x = - 3`?

Answer 1

See the entire solution process below:

Explanation:

First, we need to add `color(red)(3)` to each side of the equation to put this in standard form:

`1/3x^2 + 2x + color(red)(3) = -3 + color(red)(3)`

`1/3x^2 + 2x + 3 = 0`

Now, we can factor this as:

`(1/3x + 1)(x + 3) = 0`

Now, we can solve each term for `0` to find the solutions for `x`:

Solution 1)

`1/3x + 1 = 0`

`1/3x + 1 - color(red)(1) = 0 - color(red)(1)`

`1/3x + 0 = -1`

`1/3x = -1`

`color(red)(3) xx 1/3x = color(red)(3) xx -1`

`cancel(color(red)(3)) xx 1/color(red)(cancel(color(black)(3)))x = -3`

`x = -3`

Solution 2)

`x + 3 = 0`

`x + 3 - color(red)(3) = 0 - color(red)(3)`

`x + 0 = -3`

`x = -3`

The solution is `x = -3`