How do you solve #2x^2 - 10x + 7 = 0#?

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Answer 1 · 2015-08-15T12:29:40

The solutions are:
#color(blue)(x=(5+sqrt(11))/2#

#color(blue)(x=(5-sqrt(11))/2#

#2x^2−10x+7=0#

The equation is of the form #color(blue)(ax^2+bx+c=0# where:
#a=2, b=-10, c=7#

The Discriminant is given by:

#color(blue)(Delta=b^2-4*a*c#

# = (-10)^2-(4* 2 * 7)#

# = 100 -56=44#

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

#x = (-(-10)+-sqrt(44))/(2*2) = (10+-2sqrt(11))/4#

#x=(cancel2( 5+-sqrt(11)))/cancel4#

#color(blue)(x=(5+sqrt(11))/2#

#color(blue)(x=(5-sqrt(11))/2#