How do you solve #2(7x + 18) − 1 = (x + 6)^2#?

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Answer 1 · 2018-03-12T03:28:36

The solution is #x=1#.

Expand the multiplication and then factor the leftover polynomial:

#color(red)2(7x + 18) − 1 = (x + 6)^2#

#color(red)2*7x+color(red)2*18-1=(x+6)^2#

#14x+36-1=(x+6)^2#

#14x+35=(x+6)(x+6)#

#14x+35=x^2+6x+6x+36#

#14x+35=x^2+12x+36#

#35=x^2-2x+36#

#0=x^2-2x+1#

#0=(x-1)^2#

#sqrt0=sqrt((x-1)^2)#

#0=x-1#

#x=1#