How do you solve 11v ^ { 2} - 7v + 19= 9?

2 Answers
Nov 23, 2017

v = (7 +- sqrt(-391))/22

Explanation:

11v^2 - 7v + 19 = 9

The 1st thing we do is to get 0 on one side of the equation so that we can try to factor it (or use quadratic formula if not possible to factor). So we move the 9 to the other side of the equation.

11v^2 - 7v + 10 = 0

This equation is in standard form, or ax^2 + bx + c = 0

Now we can try to factor it. We have to find two numbers that multiply up to a * c (or 11 * 10) AND add up to b, or -7.

So 2 numbers that multiply to 110 and add up to -7. There's NO number that does so!

So in this case we have to use the quadratic formula.
The quadratic formula equation is:
v = (-b+- sqrt(b^2 - 4ac))/(2a)
We know that a = 11, b = -7, and c = 10, so let's put these numbers in the formula.

v = (-(-7) +- sqrt((-7)^2 - 4(11)(10)))/(2(11))
v = (7 +- sqrt(49 - 4(110)))/22
v = (7 +- sqrt(49 - 440))/22
v = (7 +- sqrt(-391))/22

Nov 23, 2017

x = (7 + sqrt(489))/(22) , x = (7 - sqrt(489))/(22)

Explanation:

Given:
11v^2 - 7v + 19 = 9
Next, we subtract the coefficients;
11v^2 - 7v + 19 - 9 = 0
11v^2 - 7v + 10 = 0

We proceed to solve this question using the formula:

ax^2 + bx + c = 0

(-b +- sqrt(b^2 - 4ac))/(2a)

Substituting the values of a,b and c from 11v^2 - 7v +10 = 0;
(-(-7) +- sqrt((-7)^2 - 4*(11)*(10)))/(2*11)
((7) +- sqrt(-391))/(22)

Therefore, the values of x are:
x = (7 + sqrt(391))/(22)i
x = (7 - sqrt(391))/(22)i

Where i denotes a complex number.