Question 242786
{{{sqrt(p^2-3p+16)=p+1}}} Start with the given equation.



{{{p^2-3p+16=(p+1)^2}}} Square both sides.



{{{p^2-3p+16=p^2+2p+1}}} FOIL



{{{-3p+16=2p+1}}} Subtract {{{p^2}}} from both sides.



{{{-3p=2p+1-16}}} Subtract {{{16}}} from both sides.



{{{-3p-2p=1-16}}} Subtract {{{2p}}} from both sides.



{{{-5p=1-16}}} Combine like terms on the left side.



{{{-5p=-15}}} Combine like terms on the right side.



{{{p=(-15)/(-5)}}} Divide both sides by {{{-5}}} to isolate {{{p}}}.



{{{p=3}}} Reduce.



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Answer:


So the solution is {{{p=3}}}