`v^2 - 14v = -49` Solve the equation.
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 = a2 + 2ab + b2
we 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.