Question

How do you solve `x^2-x=90`?

Answer 1

`x=10,-9`

Explanation:

On the left, we have what appears to be a quadratic, so we can set it equal to zero to find its roots.

We can subtract `90` from both sides to get

`x^2-x-90=0`

To factor this business on the left, let's do a little thought experiment:

What two numbers sum up to `-1` (coefficient on `x` term) and have a product of `-90` (constant term)?

After some trial and error, we arrive at `-10` and `9`. Thus, our quadratic can be factored as

`(x-10)(x+9)=0`

To solve from here, we can use the Zero Product Property. If the product of two things is equal to zero, one or both of those things must be equal to zero.

Let's set both of them equal to zero to get

`x=10` and `x=-9`

Hope this helps!

Answer 2

`x=-9`

`x=10`

Explanation:

Solve meaning factor:

`x^2-x=90`

`x^2-x-90=0`

Find 2 numbers such that their sum is -1 and their product is 90:

`a+b=-1` and `a*b=90`

`a=9, b=-10`

`x^2-x-90=0`

`(x+9)(x-10)=0`

`x+9=0`

`x=-9`

`x-10=0`

`x=10`