SOLUTION: solve equation by completing the square p^2-8+12=0 this is not from the text book but from homework assignment.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: solve equation by completing the square p^2-8+12=0 this is not from the text book but from homework assignment.      Log On


   

Question 150503This question is from textbook
: solve equation by completing the square
p^2-8+12=0
this is not from the text book but from homework assignment. This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that the equation is p%5E2-8p%2B12=0+



p%5E2-8p%2B12 Start with the given expression



Take half of the p coefficient -8 to get -4 (ie %281%2F2%29%28-8%29=-4).

Now square -4 to get 16 (ie %28-4%29%5E2=%28-4%29%28-4%29=16)




p%5E2-8p%2B16-16%2B12 Now add and subtract this value inside the parenthesis. Notice how 16-16=0. Since we're adding 0, we're not changing the equation.



%28p-4%29%5E2-16%2B12 Now factor p%5E2-8p%2B16 to get %28p-4%29%5E2


%28p-4%29%5E2-4 Combine like terms




So after completing the square, p%5E2-8p%2B12 becomes %28p-4%29%5E2-4.


In other words, p%5E2-8p%2B12=%28p-4%29%5E2-4


So p%5E2-8p%2B12=0 is equivalent to %28p-4%29%5E2-4=0



%28p-4%29%5E2-4=0 Start with the given equation.


%28p-4%29%5E2=0%2B4 Add 4 to both sides.


%28p-4%29%5E2=4 Combine like terms on the right side.


p-4=0%2B-sqrt%284%29 Take the square root of both sides.


p-4=sqrt%284%29 or p-4=-sqrt%284%29 Break up the expression


p-4=2 or p-4=-2 Take the square root of 4 to get 2


p=4%2B2 or p=4-2 Add 4 to both sides.


p=6 or p=2 Combine like terms.



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Answer:


So the solution is p=6 or p=2