Question

How do you use the quadratic formula to solve `x^2+5=4x`?

Answer 1

The quadratic formula:
`(-b+-sqrt(b^2-4ac))/(2a)`
can be used to find root solutions to quadratics in the form
`ax^2+bx+c = 0`

So first we need to convert the given equation into this form:
`x^2+5 = 4x`

`rarr x^2-4x+5 = 0`

Solutions are
`x= (-(-4) +- sqrt((-4)^2 -4(1)(5)))/(2(1))`

`x= 2+-sqrt((-4))/2`

Since the discriminant is negative
there are no Real value solutions to this equation
but within Complex numbers, the solution is
`x=2+-i`