Question 215124
There are two ways to do this:


Method # 1





{{{x^2+18x+81=16}}} Start with the given equation.



{{{x^2+18x+81-16=0}}} Get every term to the left side.



{{{x^2+18x+65=0}}} Combine like terms.



Notice that the quadratic {{{x^2+18x+65}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=1}}}, {{{B=18}}}, and {{{C=65}}}



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



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



{{{x = (-(18) +- sqrt( (18)^2-4(1)(65) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=18}}}, and {{{C=65}}}



{{{x = (-18 +- sqrt( 324-4(1)(65) ))/(2(1))}}} Square {{{18}}} to get {{{324}}}. 



{{{x = (-18 +- sqrt( 324-260 ))/(2(1))}}} Multiply {{{4(1)(65)}}} to get {{{260}}}



{{{x = (-18 +- sqrt( 64 ))/(2(1))}}} Subtract {{{260}}} from {{{324}}} to get {{{64}}}



{{{x = (-18 +- sqrt( 64 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (-18 +- 8)/(2)}}} Take the square root of {{{64}}} to get {{{8}}}. 



{{{x = (-18 + 8)/(2)}}} or {{{x = (-18 - 8)/(2)}}} Break up the expression. 



{{{x = (-10)/(2)}}} or {{{x =  (-26)/(2)}}} Combine like terms. 



{{{x = -5}}} or {{{x = -13}}} Simplify. 



So the solutions are {{{x = -5}}} or {{{x = -13}}} 

  


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Method # 2



{{{x^2+18x+81=16}}} Start with the given equation.



{{{(x+9)^2=16}}} Factor the left side



{{{x+9=""+-sqrt(16)}}} Take the square root of both sides.



{{{x+9=sqrt(16)}}} or {{{x+9=-sqrt(16)}}} Break up the "plus/minus" to form two equations.



{{{x+9=4}}} or {{{x+9=-4}}}  Take the square root of {{{16}}} to get {{{4}}}.



{{{x=-9+4}}} or {{{x=-9-4}}} Subtract {{{9}}} from both sides.



{{{x=-5}}} or {{{x=-13}}} Combine like terms.



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Answer:



So the solutions are {{{x=-5}}} or {{{x=-13}}} (which is what we got earlier).