Question 190115


{{{y^2-18y=-81}}} Start with the given equation.



{{{y^2-18y+81=0}}} Add 81 to both sides.



Notice we have a quadratic equation in the form of {{{ay^2+by+c}}} where {{{a=1}}}, {{{b=-18}}}, and {{{c=81}}}



Let's use the quadratic formula to solve for y



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



{{{y = (-(-18) +- sqrt( (-18)^2-4(1)(81) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=-18}}}, and {{{c=81}}}



{{{y = (18 +- sqrt( (-18)^2-4(1)(81) ))/(2(1))}}} Negate {{{-18}}} to get {{{18}}}. 



{{{y = (18 +- sqrt( 324-4(1)(81) ))/(2(1))}}} Square {{{-18}}} to get {{{324}}}. 



{{{y = (18 +- sqrt( 324-324 ))/(2(1))}}} Multiply {{{4(1)(81)}}} to get {{{324}}}



{{{y = (18 +- sqrt( 0 ))/(2(1))}}} Subtract {{{324}}} from {{{324}}} to get {{{0}}}



{{{y = (18 +- sqrt( 0 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{y = (18 +- 0)/(2)}}} Take the square root of {{{0}}} to get {{{0}}}. 



{{{y = (18 + 0)/(2)}}} or {{{y = (18 - 0)/(2)}}} Break up the expression. 



{{{y = (18)/(2)}}} or {{{y =  (18)/(2)}}} Combine like terms. 



{{{y = 9}}} or {{{y = 9}}} Simplify. 



So the answer is {{{y = 9}}}