Question 201591
{{{x^2+8x+144=16/9}}} Start with the given equation.



{{{9*x^2+9*8x+9*144=cross(9)*(16/cross(9))}}} Multiply EVERY term by the LCD 9 to clear out the fraction.



{{{9x^2+72x+1296=16}}} Multiply and simplify



{{{9x^2+72x+1296-16=0}}} Subtract 16 from both sides.



{{{9x^2+72x+1280=0}}} Combine like terms.



Notice that the quadratic {{{9x^2+72x+1280}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=9}}}, {{{B=72}}}, and {{{C=1280}}}



Let's use the quadratic formula to solve for "x":



{{{x = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{x = (-(72) +- sqrt( (72)^2-4(9)(1280) ))/(2(9))}}} Plug in  {{{A=9}}}, {{{B=72}}}, and {{{C=1280}}}



{{{x = (-72 +- sqrt( 5184-4(9)(1280) ))/(2(9))}}} Square {{{72}}} to get {{{5184}}}. 



{{{x = (-72 +- sqrt( 5184-46080 ))/(2(9))}}} Multiply {{{4(9)(1280)}}} to get {{{46080}}}



{{{x = (-72 +- sqrt( -40896 ))/(2(9))}}} Subtract {{{46080}}} from {{{5184}}} to get {{{-40896}}}



{{{x = (-72 +- sqrt( -40896 ))/(18)}}} Multiply {{{2}}} and {{{9}}} to get {{{18}}}. 



{{{x = (-72 +- 24i*sqrt(71))/(18)}}} 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 = (-72+24i*sqrt(71))/(18)}}} or {{{x = (-72-24i*sqrt(71))/(18)}}} Break up the expression.  



So the solutions are {{{x = (-72+24i*sqrt(71))/(18)}}} or {{{x = (-72-24i*sqrt(71))/(18)}}}