How do you solve #|x ^ { 2} + 2x - 24| = 24#?

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Answer 1 · 2017-10-22T18:29:00

Let's have a look.

Given,

#color(red)(|x^2+2x-24|=24)#

#:.x^2+2x-24=+-24#

Now, the two equations obtained are:

#x^2+2x-24=+24#..........(1).

#:.color(red)(x^2+2x-48=0)#

#:.(x+8)(x-6)=0#

So, either #x=6# or #x=-8#.

&

#x^2+2x-24=-24#..........(2).

#:.color(red)(x^2+2x=0)#

#:.x(x+2)=0#

So, either #x=-2# or #x=0#.

Therefore, the four solutions of #x# are #color(red)(-8,-2,0,6)#. (Answer).