Question 150503
I'm assuming that the equation is {{{p^2-8p+12=0 }}}




{{{p^2-8p+12}}} Start with the given expression




Take half of the p coefficient {{{-8}}} to get {{{-4}}} (ie {{{(1/2)(-8)=-4}}}).


Now square {{{-4}}} to get {{{16}}} (ie {{{(-4)^2=(-4)(-4)=16}}})





{{{p^2-8p+16-16+12}}} 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.




{{{(p-4)^2-16+12}}} Now factor {{{p^2-8p+16}}} to get {{{(p-4)^2}}}



{{{(p-4)^2-4}}} Combine like terms





So after completing the square, {{{p^2-8p+12}}} becomes {{{(p-4)^2-4}}}.



In other words, {{{p^2-8p+12=(p-4)^2-4}}}



So {{{p^2-8p+12=0}}} is equivalent to {{{(p-4)^2-4=0}}}




{{{(p-4)^2-4=0}}} Start with the given equation.



{{{(p-4)^2=0+4}}} Add {{{4}}} to both sides.



{{{(p-4)^2=4}}} Combine like terms on the right side.



{{{p-4=0+-sqrt(4)}}} Take the square root of both sides.



{{{p-4=sqrt(4)}}} or {{{p-4=-sqrt(4)}}} Break up the expression



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



{{{p=4+2}}} 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}}}