How do you solve $2x^2 - 2x - 1 = 0$ ?

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Answer 1 · 2015-10-10T06:26:55

The solutions are:
$color(blue)(x= (1+sqrt(3))/2$

$color(blue)(x= (1-sqrt(3))/2$

$2x^2-2x-1=0$

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

The Discriminant is given by:
$Delta=b^2-4*a*c$
$= (-2)^2-(4*2*(-1))$
$= 4+8= 12$

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

$x = (-(-2)+-sqrt(12))/(2*2) = (2+-2sqrt(3))/4$

$(2+-2sqrt(3))/4= (cancel2(1+-sqrt(3)))/cancel4$

$= (1+-sqrt(3))/2$

The solutions are:
$color(blue)(x= (1+sqrt(3))/2$

$color(blue)(x= (1-sqrt(3))/2$

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