Question 214177
{{{x(x-8)= -15}}} Start with the given equation



{{{x^2-8x= -15}}} Distribute



{{{x^2-8x+15=0}}} Add 15 to both sides.



Notice we have a quadratic in the form of {{{ax^2+bx+c}}} where {{{a=1}}}, {{{b=-8}}}, and {{{c=15}}}



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)(15) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=-8}}}, and {{{c=15}}}



{{{x = (8 +- sqrt( (-8)^2-4(1)(15) ))/(2(1))}}} Negate {{{-8}}} to get {{{8}}}. 



{{{x = (8 +- sqrt( 64-4(1)(15) ))/(2(1))}}} Square {{{-8}}} to get {{{64}}}. 



{{{x = (8 +- sqrt( 64-60 ))/(2(1))}}} Multiply {{{4(1)(15)}}} to get {{{60}}}



{{{x = (8 +- sqrt( 4 ))/(2(1))}}} Subtract {{{60}}} from {{{64}}} to get {{{4}}}



{{{x = (8 +- sqrt( 4 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



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



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



{{{x = (10)/(2)}}} or {{{x =  (6)/(2)}}} Combine like terms. 



{{{x = 5}}} or {{{x = 3}}} Simplify. 



So the answers are {{{x = 5}}} or {{{x = 3}}}