Solve the equation by completing the square

Question

Solve the equation by completing the square please show how you got the answer so I can get a clear understanding for future problems like this

p^2 + 4p = 1

Answer 1

p^2 + 4p    =  1

 

p^2 + 4p  +  4 = 1 + 4  <---- take half of the linear coefficient, which is 4 in bold above;

                                            then square that. So half of 4 is 2. 2*2 = 4

 

(  p  +     2   )(p    +    2  ) = 5 <---- factors left side, combines like terms on right side

 

(p + 2)^2 = 5

 

p+2 = +or- sqrt(5)

 

p = -2 +or- sqrt(5)

 

 

check:

 

    [-2 + sqrt(5) ]^2 + 4( -2 + sqrt(5) ) =

    [4 + -4*sqrt(5) + 5] + 4(-2 + sqrt(5)) =

  [ 9 + -4*sqrt(5)] + -8 + 4*sqrt(5) = 1  <---- 4*sqrt(5) cancels out

   positive case checks out!!!

 

 

  [-2 - sqrt(5)]^2 + 4 ( -2 - sqrt(5)) =

  [ 4 +4*sqrt(5) + 5] + (-8 - 4*sqrt(5)) =

   9 + 4*Sqrt(5) + -8 - 4*sqrt(5) = 1 <--- 4*sqrt(5) cancels out

 

The two solutions are  -2 +or- sqrt(5)

 

Tried , tested, checked, verified,and proven to be correct.