Question 211375


{{{y^2-12y+36=100}}} Start with the given equation.



{{{y^2-12y+36-100=0}}} Get every term to the left side.



{{{y^2-12y-64=0}}} Combine like terms.



Notice that the quadratic {{{y^2-12y-64}}} is in the form of {{{Ay^2+By+C}}} where {{{A=1}}}, {{{B=-12}}}, and {{{C=-64}}}



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



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



{{{y = (-(-12) +- sqrt( (-12)^2-4(1)(-64) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=-12}}}, and {{{C=-64}}}



{{{y = (12 +- sqrt( (-12)^2-4(1)(-64) ))/(2(1))}}} Negate {{{-12}}} to get {{{12}}}. 



{{{y = (12 +- sqrt( 144-4(1)(-64) ))/(2(1))}}} Square {{{-12}}} to get {{{144}}}. 



{{{y = (12 +- sqrt( 144--256 ))/(2(1))}}} Multiply {{{4(1)(-64)}}} to get {{{-256}}}



{{{y = (12 +- sqrt( 144+256 ))/(2(1))}}} Rewrite {{{sqrt(144--256)}}} as {{{sqrt(144+256)}}}



{{{y = (12 +- sqrt( 400 ))/(2(1))}}} Add {{{144}}} to {{{256}}} to get {{{400}}}



{{{y = (12 +- sqrt( 400 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{y = (12 +- 20)/(2)}}} Take the square root of {{{400}}} to get {{{20}}}. 



{{{y = (12 + 20)/(2)}}} or {{{y = (12 - 20)/(2)}}} Break up the expression. 



{{{y = (32)/(2)}}} or {{{y =  (-8)/(2)}}} Combine like terms. 



{{{y = 16}}} or {{{y = -4}}} Simplify. 



So the solutions are {{{y = 16}}} or {{{y = -4}}}