Solve the equation by completing the square

Question

V^2+6v-8=11

Answer 1

v² - 6v - 8 = 11

v² - 6v + 9 - 8 = 11 + 9

v² - 6v + 9 = 11 + 9 + 8

(v + 3)² = 28

(v + 3) = +/- sqrt(28)

v = -3 +/- 2 * sqrt(7)   

2 real roots

You can also check the answer by using the quadratic formula.

Any questions?

 

Answer 2

Hello,

v² + 6v - 8 = 11 

v² + 6v = 19                          <---------Subtract 8 from both sides 


v² + 6v        = 19                   <---------Leave room for missing term for trinomial in order to finish

v² + 1/2 (6v)  = 19                 <---------Use 1/2 to come up with the third term and then SQUARE IT. 


v² + 6v + 9 = 28                    <---------When we add the nine to the left side it must be done to the right. 


Factor the left side of your equation: 


v² + 6v + 9 = 28                   <----------This is just the above equation but now we need to factor.

(v + 3)² = 28                         <----------This is the left side of your equation factored. 
  _____          __
√(v + 3)²  = √28                   <----------Using sq rt helps to remove the radical and we must do to both sides. PLEASE NOTE: The radical on the left goes around the entire expression of "v + 3"

                __
 v + 3 = √28                          <---------Now, we must simplify radical and set to plus or minus 
                   ____ 
v + 3 =  ± √4 * 7                   <---------√28 reduces to 2√7
                   __
v + 3 = ±2√7   

v = -3 ±2√7                          <---------The square is completed and reduced as far as possible. 



I hope I have helped you by showing the process step by step and wish you a great weekend. If you have any further questions, feel free to comment below. 

Answer 3

Hi T.

 

To complete the square, we need to force the left side to be (x-a)², and keep the whole equation balanced.

 

If we started with  v²+6v,  to complete the square we would divide 6 by 2, then square the answer to get the constant to add at the end.

 

6/2 = 3

3² = 9

 

So we could fill in a constant to make the v²+6v  a complete square.  It would be:

 

v²+6v+9  because this is (x+3)²

 

So that is our goal.  To make the left side (x+3)² without unbalancing the equation.

 

 

Start by adding 8 to both sides.  This gives you

 

v²+6v  = 19

 

Now add the 9 (that completes the square on the left) to both sides.

 

v²+6v+9 = 19 + 9

 

 

Now represent the left side as the perfect square we just forced it to be

 

(v+3)² = 28

 

 

That was the hard part.  Now just take the square root of both sides.

 

v+3 = + √28

 

And the last thing is to isolate v by subtracting 3 from both sides.

 

v = -3 + √28

 

And your teacher probably wants the radical in most-simplified form, so the final answer will be

 

v = -3 + 2√7