Question 531609


{{{x^2-10x+16=0}}} Start with the given equation.



Notice that the quadratic {{{x^2-10x+16}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=1}}}, {{{B=-10}}}, 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 = (-(-10) +- sqrt( (-10)^2-4(1)(16) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=-10}}}, and {{{C=16}}}



{{{x = (10 +- sqrt( (-10)^2-4(1)(16) ))/(2(1))}}} Negate {{{-10}}} to get {{{10}}}. 



{{{x = (10 +- sqrt( 100-4(1)(16) ))/(2(1))}}} Square {{{-10}}} to get {{{100}}}. 



{{{x = (10 +- sqrt( 100-64 ))/(2(1))}}} Multiply {{{4(1)(16)}}} to get {{{64}}}



{{{x = (10 +- sqrt( 36 ))/(2(1))}}} Subtract {{{64}}} from {{{100}}} to get {{{36}}}



{{{x = (10 +- sqrt( 36 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (10 +- 6)/(2)}}} Take the square root of {{{36}}} to get {{{6}}}. 



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



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



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



So the solutions are {{{x = 8}}} or {{{x = 2}}}