Question 210971
Solve by completing the square:
{{{15p^2+7p-4 = 0}}} Divide through by 15 to get the coefficient of {{{p^2}}} equal to 1.
{{{p^2+(7/15)p-4/15 = 0}}} Now add {{{4/15}}} to both sides of the equation.
{{{p^2+(7/15)p = 4/15}}} Complete the square in p by adding the square of half the p-coefficient to both sides. {{{((1/2)(7/15))^2 = 49/900}}}
{{{p^2+(7/15)p + 49/900 = (7/15)+49/900}}} Factor the left side and simplify the right side.
{{{(p+7/30)^2 = (420/900)+(49/900)}}}
{{{(p+(7/30))^2 = 469/900}}} take the square root of both sides.
{{{p+(7/30) = sqrt(469)/30}}} or {{{p+(7/30) = -sqrt(469)/30}}}Subtract {{{(7/30)}}} from both sides.
{{{p = ((-7/30)+sqrt(469))/30}}} or {{{p = ((-7/30)-sqrt(469))/30}}}
{{{p = (-7+sqrt(469))/30}}} or {{{p = (-7-sqrt(469))/30}}}