# `v^2 - 14v = -49` Solve the equation.

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v^2 - 14v = - 49

add 49 to the opposing side:

v^2 - 14v + 49

this is a perfect square trinomial so we can use the difference of 2 squares to get the answer:

(* a + b*)2 =

*2*

*a**2*

*+*

*ab + b*2we know v is a perfect square and so is 7, therefore we take the squareroot of both numbers and and make 2 answers:

for example the problem could be written as (v - 7)^2 (- because b is negative)

if you take the sqrt of (v-7)^2 you get (v-7)(v-7) which is the answer.

v^2 - 14v = -49

Move the -49 over to the left so that one side of the equation will be 0.

v^2 - 14v +49 = 0

Use the magic x or whatever way preferred to factorise the equation to get:

(v - 7) (v -7) = 0

Solve for v to get v = 7.