Question 337761
{{{(p-2)^2=4p}}} Start with the given equation.



{{{p^2-4p+4=4p}}} FOIL



{{{p^2-4p+4-4p=0}}} Subtract 4p from both sides.



{{{p^2-8p+4=0}}} Combine like terms.



Notice we have a quadratic equation in the form of {{{ap^2+bp+c}}} where {{{a=1}}}, {{{b=-8}}}, and {{{c=4}}}



Let's use the quadratic formula to solve for p



{{{p = (-b +- sqrt( b^2-4ac ))/(2a)}}} Start with the quadratic formula



{{{p = (-(-8) +- sqrt( (-8)^2-4(1)(4) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=-8}}}, and {{{c=4}}}



{{{p = (8 +- sqrt( (-8)^2-4(1)(4) ))/(2(1))}}} Negate {{{-8}}} to get {{{8}}}. 



{{{p = (8 +- sqrt( 64-4(1)(4) ))/(2(1))}}} Square {{{-8}}} to get {{{64}}}. 



{{{p = (8 +- sqrt( 64-16 ))/(2(1))}}} Multiply {{{4(1)(4)}}} to get {{{16}}}



{{{p = (8 +- sqrt( 48 ))/(2(1))}}} Subtract {{{16}}} from {{{64}}} to get {{{48}}}



{{{p = (8 +- sqrt( 48 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{p = (8 +- 4*sqrt(3))/(2)}}} Simplify the square root  (note: If you need help with simplifying square roots, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  



{{{p = (8)/(2) +- (4*sqrt(3))/(2)}}} Break up the fraction.  



{{{p = 4 +- 2*sqrt(3)}}} Reduce.  



{{{p = 4+2*sqrt(3)}}} or {{{p = 4-2*sqrt(3)}}} Break up the expression.  



So the answers are {{{p = 4+2*sqrt(3)}}} or {{{p = 4-2*sqrt(3)}}} 



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Jim