How do you solve $x²-6x+3=0$ using the quadratic formula?

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Answer 1 · 2016-06-28T18:40:52

The solutions are:
$color(blue)( x = 3 + sqrt6$

$color(blue)( x = 3 - sqrt6$

$x^2 - 6x +3 = 0$

The equation is of the form $color(blue)(ax^2+bx+c=0$ where:
$a=1, b=-6, c=3$

The Discriminant is given by:

$Delta=b^2-4*a*c$

$= (-6)^2-(4* 1 * 3)$

$= 36 - 12= 24$

The solutions are found using the formula
$x=(-b+-sqrtDelta)/(2*a)$

$x = (-(-6)+-sqrt(24))/(2*1) = (6+-sqrt(24))/2$

$sqrt24$ can be further simplified as follows:

$sqrt24 = sqrt ( 2 * 2 * 2 * 3) = sqrt ( 2 ^2 * 2 * 3 ) = 2 sqrt6$

$x= (6+-2sqrt(6))/2$

$x= (2 ( 3 +- sqrt(6)))/2$

$x= (cancel2 ( 3 +- sqrt(6)))/cancel2$

The solutions are:
$color(blue)( x = 3 + sqrt6$
$color(blue)( x = 3 - sqrt6$

How do you solve x²-6x+3=0x²-6x+3=0 using the quadratic formula?