Question

How do you solve `2x^2+5x=0` using the quadratic formula?

Answer 1

Express in the form `ax^2+bx+c=0` then apply the formula to find:

`x = 0" "` or `" "x = -5/2`

Explanation:

Given:

`2x^2+5x=0`

we can express this equation as:

`2x^2+5x+0 = 0`

This is in the form:

`ax^2+bx+c = 0`

with `a=2`, `b=5` and `c=0`

It has roots given by the quadratic formula:

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

`color(white)(x) = (-5+-sqrt((-5)^2-4(2)(0)))/(2*2)`

`color(white)(x) = (-5+-sqrt(25))/4`

`color(white)(x) = (-5+-5)/4`

So one root is:

`x = (-5+5)/4 = 0`

and the other is:

`x = (-5-5)/4 = -10/4 = -5/2`

`color(white)()`
Footnote

You really would not normally choose to use the quadratic formula in this example.

Instead note that both terms are divisible by `x`, so it factors like this:

`0 = 2x^2+5x = x(2x+5)`

Which has solutions `x=0` and `x=-5/2`