Question 351791
{{{f(x)=g(x)}}} Start with the given equation.



{{{x^2+16x+19=8x+7}}} Plug in {{{f(x)=x^2+16x+19}}} and {{{g(x)= 8x+7}}}



{{{x^2+16x+19-8x-7=0}}} Get all terms to the left side.



{{{x^2+8x+12=0}}} Combine like terms.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=1}}}, {{{b=8}}}, and {{{c=12}}}



Let's use the quadratic formula to solve for x



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



{{{x = (-(8) +- sqrt( (8)^2-4(1)(12) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=8}}}, and {{{c=12}}}



{{{x = (-8 +- sqrt( 64-4(1)(12) ))/(2(1))}}} Square {{{8}}} to get {{{64}}}. 



{{{x = (-8 +- sqrt( 64-48 ))/(2(1))}}} Multiply {{{4(1)(12)}}} to get {{{48}}}



{{{x = (-8 +- sqrt( 16 ))/(2(1))}}} Subtract {{{48}}} from {{{64}}} to get {{{16}}}



{{{x = (-8 +- sqrt( 16 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (-8 +- 4)/(2)}}} Take the square root of {{{16}}} to get {{{4}}}. 



{{{x = (-8 + 4)/(2)}}} or {{{x = (-8 - 4)/(2)}}} Break up the expression. 



{{{x = (-4)/(2)}}} or {{{x =  (-12)/(2)}}} Combine like terms. 



{{{x = -2}}} or {{{x = -6}}} Simplify. 



So the answers are {{{x = -2}}} or {{{x = -6}}}