Question 339150
{{{(x+3)^2+9(x+3)+14=0}}} Start with the given equation.



{{{x^2+6x+9+9(x+3)+14=0}}} FOIL



{{{x^2+6x+9+9x+27+14=0}}} Distribute.



{{{x^2+15x+50=0}}} Combine like terms.



Notice that the quadratic {{{x^2+15x+50}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=1}}}, {{{B=15}}}, and {{{C=50}}}



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



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



{{{x = (-(15) +- sqrt( (15)^2-4(1)(50) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=15}}}, and {{{C=50}}}



{{{x = (-15 +- sqrt( 225-4(1)(50) ))/(2(1))}}} Square {{{15}}} to get {{{225}}}. 



{{{x = (-15 +- sqrt( 225-200 ))/(2(1))}}} Multiply {{{4(1)(50)}}} to get {{{200}}}



{{{x = (-15 +- sqrt( 25 ))/(2(1))}}} Subtract {{{200}}} from {{{225}}} to get {{{25}}}



{{{x = (-15 +- sqrt( 25 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (-15 +- 5)/(2)}}} Take the square root of {{{25}}} to get {{{5}}}. 



{{{x = (-15 + 5)/(2)}}} or {{{x = (-15 - 5)/(2)}}} Break up the expression. 



{{{x = (-10)/(2)}}} or {{{x =  (-20)/(2)}}} Combine like terms. 



{{{x = -5}}} or {{{x = -10}}} Simplify. 



So the solutions are {{{x = -5}}} or {{{x = -10}}} 



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