How do you solve #2x^2 – 8x = –7# using the quadratic formula?

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Answer 1 · 2016-02-29T17:11:30

The solutions are:
#x = (4+sqrt(2))/2#
#x = (4-sqrt(2))/2#

#2x^2 -8x+7=0#

The equation is of the form #color(blue)(ax^2+bx+c=0# where:

#a=2, b=-8, c=7#

The Discriminant is given by:

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

# = (-8)^2-(4* 2 * 7)#

# = 64- 56 =8#

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

#x = (-(-8)+-sqrt(8))/(2*2) = (8+-2sqrt(2))/4#

#=( 2(4+-sqrt(2)))/4#

#=( cancel2(4+-sqrt(2)))/cancel4#

#=(4+-sqrt(2))/2#

The solutions are:
#x = (4+sqrt(2))/2#
#x = (4-sqrt(2))/2#