Question

How do you solve `x^2-10<3x`?

Answer 1

THe answer is `x in ] -2,5 [`

Explanation:

Let's rewrite the equation as

`f(x)=x^2-3x-10=(x+2)(x-5)<0`

Let's do a sign chart

`color(white)(aaaa)` `x` `color(white)(aaaa)` `-oo` `color(white)(aaaa)` `-2` `color(white)(aaaa)` `5` `color(white)(aaaa)` `+oo`

`color(white)(aaaa)` `x+2` `color(white)(aaaaa)` `-` `color(white)(aaaa)` `+` `color(white)(aaaa)` `+`

`color(white)(aaaa)` `x-5` `color(white)(aaaaa)` `-` `color(white)(aaaa)` `-` `color(white)(aaaa)` `+`

`color(white)(aaaa)` `f(x)` `color(white)(aaaaaa)` `+` `color(white)(aaaa)` `-` `color(white)(aaaa)` `+`

So, `f(x)<0` for `x in ] -2,5 [`

graph{x^2-3x-10 [-25.66, 25.65, -12.83, 12.85]}