Question

How do you solve `\frac { 18} { 75} = x ^ { 2} + x`?

Answer 1

Find the zeros by using the quadratic formula.

Explanation:

Solving implies we determine the value of `x`.

With a degree of `2`, we can assume this as a function with a parabola. Thus, we can either factor or use the quadratic formula to solve for `x`. I will be using the latter.

First off, let's bring the `18/75` to the other side of the equation, then we will equate it to `0`.

`18/75 =x^2 + x`

`0 =x^2 + x - 18/75`

Now, we will use the quadratic formula and sub in the corresponding variables.

`x = (-b+-sqrt(b^2-4ac))/(2a)`

`x = (-[1]+-sqrt([1]^2-4[1][-18/75]))/(2[1])`

Now we simplify.

`x = (-1+-sqrt(49/25))/(2)`

And we solve.

`x [+] = 1/5`

`x [-] = -6/5`

graph{x^2 + x - 18/75 [-10, 10, -5, 5]}

If we graph the equation, we can visibly see the zeros, and we are correct.

Hope this helps :)