How do you solve #x( x - 5) = 66#?

3 Answers
Bill Jorgensen
May 19, 2018

#x = 11 and -6#

Explanation:

#x(x-5) = 66#

#x^2-5x-66 =0#

#(x+6)(x-11) = 0#

#x+6 =0#

#x = -6#

and

#x - 11 =0#

#x = 11#

so: #x = 11 and -6#

Nallasivam V
May 19, 2018

#x=11#
#x=-6#

Explanation:

Given -

#x(x-5)=66#

#x^2-5x=66#

#x^2-5x+25/4=66+25/4=(264+25)/4=289/4 #

#(x-5/2)^2=289/4#

#x-5/2=+-sqrt((289)/4)=17/2#

#x=17/2+5/2=22/2=11#

#x=11#

#x=-17/2+5/2=-12/2=-6#

#x=-6#

Meave60
May 19, 2018

#x=-6,11#

Explanation:

Solve:

#x(x-5)=66#

Expand the left-hand side.

#x^2-5x=66#

Move all terms to the left-hand side.

#x^2-5x-66=0#

Factor the left-hand side.

Find two numbers that when added equal #-5# and when multiplied equal #-66#. The numbers #6# and #-11# meet the requirements.

#(x+6)(x-11)=0#

Solutions for #x#.

#x+6=0#

#x=-6#

#x-11=0#

#x=11#

#x=-6,11#

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