Question

How do you solve `x^2 - x - 30 = 0` using the quadratic formula?

Answer 1

See below for use of quadratic formula to obtain
`x=-5 or x=6`

Explanation:

For the general quadratic equation `ax^2+bx+c=0`
the quadratic formula:
`color(white)("XXX")x=(-b+-sqrt(b^2-4ac))/(2a)`
gives the solutions.

For the example: `x^2-x-30=0`
`color(white)("XXX")a=1`
`color(white)("XXX")b=-1`
`color(white)("XXX")c=-30`

Replacing the variables `a, b, c` in the general solution formula gives:
`color(white)("XXXX")x=(-(-1)+-sqrt((-1)^2-4(1)(-30)))/(2(1))`

`color(white)("XXXX")=(1+-sqrt(121))/2`

`color(white)("XXXX")=(1+-11)/2`

`rArr x=-5 or +6`