How do you solve #2x^2-11x=1#?

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Answer 1 · 2015-09-22T12:39:38

The solutions are
#color(blue)(x=(11+sqrt(129))/4#

#color(blue)(x=(11-sqrt(129))/4#

# 2x^2−11x=1#

# 2x^2−11x- 1=0#

The equation is of the form #color(blue)(ax^2+bx+c=0# where:
#a=2, b=-11, c= -1#

The Discriminant is given by:
#Delta=b^2-4*a*c#
# = (-11)^2-(4*2* (-1))#
# = 121 +8=129#

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

#x = (-(-11)+-sqrt(129))/(2*2) = (11+-sqrt(129))/4#

The solutions are
#color(blue)(x=(11+sqrt(129))/4#

#color(blue)(x=(11-sqrt(129))/4#