How do you solve #(x+6)(x-2)=9#?

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Answer 1 · 2016-03-14T17:34:44

The solutions are:
#x=3#
#x=-7#

#(x+6)(x−2)=9#

#(x) * (x) + x * (-2) +( 6) * (x) + 6 * (-2)=9#

#x^2 -2x + 6 x -12=9#

#x^2 +4x -12=9#

#x^2 +4x -12- 9= 0#

#x^2 +4x -21= 0#

The equation is of the form #color(blue)(ax^2+bx+c=0# where:
#a=1, b=4, c= -21#

The Discriminant is given by:

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

# = (4)^2-(4*1 *-21)#

# = 16 + 84= 100#

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

#x =( -4 +-sqrt(100))/( 2* 1#

#x= ( -4 +10 )/ 2 = 6/2 = 3#

#x=( -4 -10 )/ 2 = -14/2 = -7#