Question

How do you solve `x^2-7x=5` using the quadratic formula?

Answer 1

`x = (7+sqrt(69))/2`
or
`x = (7-sqrt(69))/2`

Explanation:

Given `x^2-7x =5`

Re-writing in standard form:
`color(white)("XXXX")` `1x^2-7x-5 = 0`

The general standard form for a quadratic is
`color(white)("XXXX")` `ax^2+bx+c = 0`

The quadratic formula tells us that the solution for an equation in the general form is:
`color(white)("XXXX")` `x = (-b+-sqrt(b^2-4ac))/(2a)`

Base on the re-written form of the given equation:
`a=1` `color(white)("XXXX")` `b=-7` `color(white)("XXXX")` `c=-5`

So the solution is
`color(white)("XXXX")` `x = (7+-sqrt((-7)^2-4(1)(-5)))/(2(1)`

`color(white)("XXXX")` `color(white)("XXXX")` `=(7+-sqrt(69))/2`