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

Question

1907 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:
$x=(4+-sqrt((-4)^2-4(2)(1)))/(2(2))$

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

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

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

How do you solve using the quadratic formula 2x^2 + 1 = 4x2x^2 + 1 = 4x?