Question

How do you use the quadratic formula to solve `9x^2-6x+37=0`?

Answer 1

`x = 1/3+-2i`

Explanation:

`9x^2-6x+37 = 0`

is in the form:

`ax^2+bx+c = 0`

with `a=9`, `b=-6` and `c=37`

This has zeros given by the quadratic formula:

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

`color(white)(x) = (6+-sqrt((-6)^2-4(9)(37)))/(2(9))`

`color(white)(x) = (6+-sqrt(36-36(37)))/18`

`color(white)(x) = (6+-sqrt(36(1-37)))/18`

`color(white)(x) = (6+-sqrt(-36^2))/18`

`color(white)(x) = (6+-36i)/18`

`color(white)(x) = 1/3+-2i`