Question 189241


{{{x^2+8x+5=0}}} Start with the given equation.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=1}}}, {{{b=8}}}, and {{{c=5}}}



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(1)(5) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=8}}}, and {{{c=5}}}



{{{x = (-8 +- sqrt( 64-4(1)(5) ))/(2(1))}}} Square {{{8}}} to get {{{64}}}. 



{{{x = (-8 +- sqrt( 64-20 ))/(2(1))}}} Multiply {{{4(1)(5)}}} to get {{{20}}}



{{{x = (-8 +- sqrt( 44 ))/(2(1))}}} Subtract {{{20}}} from {{{64}}} to get {{{44}}}



{{{x = (-8 +- sqrt( 44 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (-8 +- 2*sqrt(11))/(2)}}} 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) +- (2*sqrt(11))/(2)}}} Break up the fraction.  



{{{x = -4 +- sqrt(11)}}} Reduce.  



{{{x = -4+sqrt(11)}}} or {{{x = -4-sqrt(11)}}} Break up the expression.  



So the answers are {{{x = -4+sqrt(11)}}} or {{{x = -4-sqrt(11)}}} 



which approximate to {{{x=-0.683}}} or {{{x=-7.317}}}