Question 255471


{{{g^2+8g+16=0}}} Start with the given equation.



Notice that the quadratic {{{g^2+8g+16}}} is in the form of {{{Ag^2+Bg+C}}} where {{{A=1}}}, {{{B=8}}}, and {{{C=16}}}



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



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



{{{g = (-(8) +- sqrt( (8)^2-4(1)(16) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=8}}}, and {{{C=16}}}



{{{g = (-8 +- sqrt( 64-4(1)(16) ))/(2(1))}}} Square {{{8}}} to get {{{64}}}. 



{{{g = (-8 +- sqrt( 64-64 ))/(2(1))}}} Multiply {{{4(1)(16)}}} to get {{{64}}}



{{{g = (-8 +- sqrt( 0 ))/(2(1))}}} Subtract {{{64}}} from {{{64}}} to get {{{0}}}



{{{g = (-8 +- sqrt( 0 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{g = (-8 +- 0)/(2)}}} Take the square root of {{{0}}} to get {{{0}}}. 



{{{g = (-8 + 0)/(2)}}} or {{{g = (-8 - 0)/(2)}}} Break up the expression. 



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



{{{g = -4}}} or {{{g = -4}}} Reduce. 



So the solution is {{{g = -4}}}