Question 154615


{{{x^2-6x=16}}} Start with the given equation.



{{{x^2-6x-16=0}}} Subtract 16 from both sides.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=1}}}, {{{b=-6}}}, and {{{c=-16}}}



Let's use the quadratic formula to solve for x



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



{{{x = (-(-6) +- sqrt( (-6)^2-4(1)(-16) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=-6}}}, and {{{c=-16}}}



{{{x = (6 +- sqrt( (-6)^2-4(1)(-16) ))/(2(1))}}} Negate {{{-6}}} to get {{{6}}}. 



{{{x = (6 +- sqrt( 36-4(1)(-16) ))/(2(1))}}} Square {{{-6}}} to get {{{36}}}. 



{{{x = (6 +- sqrt( 36--64 ))/(2(1))}}} Multiply {{{4(1)(-16)}}} to get {{{-64}}}



{{{x = (6 +- sqrt( 36+64 ))/(2(1))}}} Rewrite {{{sqrt(36--64)}}} as {{{sqrt(36+64)}}}



{{{x = (6 +- sqrt( 100 ))/(2(1))}}} Add {{{36}}} to {{{64}}} to get {{{100}}}



{{{x = (6 +- sqrt( 100 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (6 +- 10)/(2)}}} Take the square root of {{{100}}} to get {{{10}}}. 



{{{x = (6 + 10)/(2)}}} or {{{x = (6 - 10)/(2)}}} Break up the expression. 



{{{x = (16)/(2)}}} or {{{x =  (-4)/(2)}}} Combine like terms. 



{{{x = 8}}} or {{{x = -2}}} Simplify. 



So the answers are {{{x = 8}}} or {{{x = -2}}}