Question 337763
{{{2p^2+8p=-3}}} Start with the given equation.



{{{2p^2+8p+3=0}}} Add 3 to both sides.



Notice we have a quadratic equation in the form of {{{ap^2+bp+c}}} where {{{a=2}}}, {{{b=8}}}, and {{{c=3}}}



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(2)(3) ))/(2(2))}}} Plug in  {{{a=2}}}, {{{b=8}}}, and {{{c=3}}}



{{{p = (-8 +- sqrt( 64-4(2)(3) ))/(2(2))}}} Square {{{8}}} to get {{{64}}}. 



{{{p = (-8 +- sqrt( 64-24 ))/(2(2))}}} Multiply {{{4(2)(3)}}} to get {{{24}}}



{{{p = (-8 +- sqrt( 40 ))/(2(2))}}} Subtract {{{24}}} from {{{64}}} to get {{{40}}}



{{{p = (-8 +- sqrt( 40 ))/(4)}}} Multiply {{{2}}} and {{{2}}} to get {{{4}}}. 



{{{p = (-8 +- 2*sqrt(10))/(4)}}} 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*sqrt(10))/(4)}}} or {{{p = (-8-2*sqrt(10))/(4)}}} Break up the expression. 



{{{p = (-4+sqrt(10))/(2)}}} or {{{p = (-4-sqrt(10))/(2)}}} Reduce. 



So the answers are {{{p = (-4+sqrt(10))/(2)}}} or {{{p = (-4-sqrt(10))/(2)}}} 



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Jim