How do you solve #w- 1= \sqrt { - 19+ 7w }#?

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Answer 1 · 2018-03-19T23:13:04

The solutions are #w=4, 5#.

Square both sides of the equation, combine like terms, then factor the new quadratic. Here's what that process looks like:

#w-1=sqrt(-19+7w)#

#(w-1)^2=(sqrt(-19+7w))^2#

#(w-1)^2=-19+7w#

#(w-1)(w-1)=-19+7w#

#w^2-w-w+1=-19+7w#

#w^2-2w+1=-19+7w#

#w^2-9w+1=-19#

#w^2-9w+20=0#

#(w-4)(w-5)=0#

#w=4,5#

Those are the solutions. Hope this helped!