Question 46158
Solve by "completing the square":
{{{3p^2-12p-10 = 0}}} Your first step is correct! Divide everything by 3 to make the coefficient of {{{P^2}}} = 1.
{{{p^2-4p-10/3 = 0}}} Now add {{{10/3}}} from both sides.
{{{p^2-4p = 10/3}}} Now add the "square of half the coefficient of p" to both sides of the equation, that's {{{(-4/2)^2 = 4}}}.
{{{p^2-4p+4 = 4+10/3}}} Now factor the left side and simplify the right side.
{{{(p-2)(p-2) = 22/3}}}
{{{(p-2)^2 = 22/3}}} Take the square root of both sides.
{{{p-2 = +sqrt(22/3)}}} or {{{p-2 = -sqrt(22/3)}}} Add 2 to both sides of these two equations.
{{{p = 2+-sqrt(22/3)}}}