Question 171872


{{{5y^2+5y=9}}} Start with the given equation.



{{{5y^2+5y-9=0}}} Subtract 9 from both sides.



Notice we have a quadratic equation in the form of {{{ay^2+by+c}}} where {{{a=5}}}, {{{b=5}}}, and {{{c=-9}}}



Let's use the quadratic formula to solve for y



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



{{{y = (-(5) +- sqrt( (5)^2-4(5)(-9) ))/(2(5))}}} Plug in  {{{a=5}}}, {{{b=5}}}, and {{{c=-9}}}



{{{y = (-5 +- sqrt( 25-4(5)(-9) ))/(2(5))}}} Square {{{5}}} to get {{{25}}}. 



{{{y = (-5 +- sqrt( 25--180 ))/(2(5))}}} Multiply {{{4(5)(-9)}}} to get {{{-180}}}



{{{y = (-5 +- sqrt( 25+180 ))/(2(5))}}} Rewrite {{{sqrt(25--180)}}} as {{{sqrt(25+180)}}}



{{{y = (-5 +- sqrt( 205 ))/(2(5))}}} Add {{{25}}} to {{{180}}} to get {{{205}}}



{{{y = (-5 +- sqrt( 205 ))/(10)}}} Multiply {{{2}}} and {{{5}}} to get {{{10}}}. 



{{{y = (-5+sqrt(205))/(10)}}} or {{{y = (-5-sqrt(205))/(10)}}} Break up the expression.  



So the answers are {{{y = (-5+sqrt(205))/(10)}}} or {{{y = (-5-sqrt(205))/(10)}}} 



which approximate to {{{y=0.932}}} or {{{y=-1.932}}} 



So to the nearest hundredth, the answers are {{{y=0.9}}} or {{{y=-1.9}}}