49v^2-75v=-24-5vfactoring

We'll use another method to solve the
quadratic equation.

First, we'll have to
re-write the equation.

We'll add 5v both
sides:

49v^2 - 75v + 5v =
-24

Now, we'll add 24 both
sides:

49v^2 - 75v + 5v + 24 =
0

We'll combine like
terms:

49v^2 - 70v + 24 =
0

From this point, we can calculate the roots using 2
methods

First
method:

We'll apply the quadratic
formula:

v1 = [-b+sqrt(b^2 -
4ac)]/2a

v1 =
[70+sqrt(196)]/98

v1 =
(70+14)/98

v1 = 84/98

v1 =
42/49

v1 =
6/7

v2 =
(70-14)/98

v2 = 56/98

v2 =
28/49

v2 =
4/7

Second
method:

We'll complete the
square

49v^2 - 70v + 24 =
0

[(7v)^2 - 7*2*5v + 5^2] - 5^2 + 24 =
0

(7v-5)^2 - 1 = 0

We'll solve
the difference of squares using the formula:

a^2 - b^2 =
(a-b)(a+b)

(7v-5)^2 - 1 =
(7v-5-1)(7v-5+1)

(7v-5)^2 - 1 =
(7v-6)(7v-4)

But, (7v-5)^2 - 1 = 0, so (7v-6)(7v-4) =
0

We'll set each factor as
0:

7v - 6 = 0

We'll add 6 both
sides:

7v = 6

We'll divide by
7:

v =
6/7

7v-4 =
0

We'll add 4 both sides:

7v =
4

v =
4/7