Question 948127

{{{x^2 + 20 = 2x}}} ...first write it in {{{ax^2+bx+c=0}}} form

{{{x^2-2x + 20 = 0}}}

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} ..in your case {{{a=1}}}, {{{b=-2}}}, and {{{c=20}}}


{{{x = (-(-2) +- sqrt( (-2)^2-4*1*20 ))/(2*1) }}} 

{{{x = (2 +- sqrt( 4-80 ))/2 }}} 

{{{x = (2 +- sqrt( -4*19 ))/2 }}} 

{{{x = (2 +- 2sqrt(19 )*i)/2 }}} 

{{{x = (cross(2)1 +- cross(2)1sqrt(19 )*i)/cross(2)1 }}} 

{{{x = (1 +- sqrt(19 )*i) }}} 

so, we have complex solutions which means there is no x-intercepts:

{{{x = 1 + sqrt(19 )*i }}}

{{{x = 1 - sqrt(19 )*i }}}


{{{ graph( 600, 600, -10, 10, -10, 55, x^2-2x + 20 ) }}}