How do you solve using the quadratic formula #2x^2 + 1 = 4x#?

Question

1705 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-05T12:27:01

To use the quadratic formula we must first rearrange the quadratic equation into the form:
#ax^2+bx+c = 0#

#2x^2+1=4x#

#2x^2-4x+1 = 0#

The quadratic formula for roots is

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

for the given example:
#x=(4+-sqrt((-4)^2-4(2)(1)))/(2(2))#

#= 1+-sqrt(8)/4#

#=1+-sqrt(2)/2#

#x=1+1/sqrt(2) " or " x=1-1/sqrt(2)#