How do you solve #x^2 - x = 42#?

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Answer 1 · 2016-03-15T15:21:05

The solutions are:
#x = 7#

#x=-6#

#x^2 - x =42#

#x^2 - x - 42 =0#

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

#a=1, b=-1, c=-42#

The Discriminant is given by:

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

# = (-1)^2-(4*1* -42)#

# = 1 + 168=169 #

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

#x = (-(-1)+-sqrt(169))/(2*1) = (1+-13)/2#

#x= (1+13)/2 = 14/2 = 7#

#x= (1-13)/2 = -12/2 =-6#