Question 171820


{{{2x^2+8x-3=0}}} Start with the given equation.



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



Let's use the quadratic formula to solve for x



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



{{{x = (-(8) +- sqrt( (8)^2-4(2)(-3) ))/(2(2))}}} Plug in  {{{a=2}}}, {{{b=8}}}, and {{{c=-3}}}



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



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



{{{x = (-8 +- sqrt( 64+24 ))/(2(2))}}} Rewrite {{{sqrt(64--24)}}} as {{{sqrt(64+24)}}}



{{{x = (-8 +- sqrt( 88 ))/(2(2))}}} Add {{{64}}} to {{{24}}} to get {{{88}}}



{{{x = (-8 +- sqrt( 88 ))/(4)}}} Multiply {{{2}}} and {{{2}}} to get {{{4}}}. 



{{{x = (-8 +- 2*sqrt(22))/(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>)  



{{{x = (-8+2*sqrt(22))/(4)}}} or {{{x = (-8-2*sqrt(22))/(4)}}} Break up the expression.  



So the answers are {{{x = (-8+2*sqrt(22))/(4)}}} or {{{x = (-8-2*sqrt(22))/(4)}}} 



which approximate to {{{x=0.345}}} or {{{x=-4.345}}}