How do you solve v^ { 2} - 6v = 35v26v=35 by completing the square?

2 Answers
Apr 17, 2017

By completing the square, we see that

v^2-6v-35=v^2-6v+9-44=(v-3)^2-44v26v35=v26v+944=(v3)244

so in order to solve it we can solve

(v-3)^2=44(v3)2=44

By setting x=v-3x=v3, we can solve x^2=44 Rightarrow x=2pm sqrt(11)x2=44x=2±11, hence v-3=sqrt(11) Rightarrow v=3+sqrt 11v3=11v=3+11

Apr 17, 2017

v=2sqrt(11)+3v=211+3

Explanation:

Completing the square is a process where one would manipulate the polynomial such that it could be factored into the form (variable +/- number) squared.

The trick to finding the third term in the polynomial is (b/2)^2(b2)2. Thus, for this equation, we want the left side to be v^2-6v+9v26v+9.

With that in mind, we add 9 to both sides, and simplify.
v^2-6v+9=44v26v+9=44
(v-3)^2=44(v3)2=44

Now we can take the square root of both sides, and solve for v.
v-3=sqrt(44)v3=44
v=sqrt(44)+3v=44+3
v=2sqrt(11)+3v=211+3