Question

How do you solve `x^2-175=0` using the quadratic formula?

Answer 1

`x=+-5sqrt(7)`

Explanation:

The quadratic formula for an equation in the form:
`color(white)("XXX")color(red)(a)x^2color(blue)(+b)x+color(green)(c)=0`
gives us the solutions:
`color(white)("XXX")x=(-color(blue)(b)+-sqrt(color(blue)(b)-4(color(red)(a)color(green)(c))))/(2color(red)(a))`

`x^2-175=0` is equivalent to
`color(white)("XXX")color(red)(1)x^2+color(blue)(0)x+color(green)(""(-175))=0`

So the solutions are
`color(white)("XXX")x=(-color(blue)(0)+-sqrt(color(blue)(0)-4 * (color(red)(1) * color(green)(""(-175)))))/(2 * color(red)(1))`

`color(white)("XXXX")=+-sqrt(700)/2`

`color(white)("XXXX")=+-(10sqrt(7))/2`

`color(white)("XXXX")=+-5sqrt(7)`