Question 703407


{{{sqrt(2-x) = x+4}}}.......square both sides


{{{(sqrt(2-x))^2 = (x+4)^2}}}

{{{2-x= x^2+8x+16}}}

{{{0= x^2+8x+x+16-2}}}

{{{ x^2+9x+14=0}}}......use quadratic formula to find solutions


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} ..{{{a=1}}}, {{{b=9}}} and {{{c=14}}}


{{{x = (-9 +- sqrt( 9^2-4*1*14 ))/(2*1) }}} 


{{{x = (-9 +- sqrt( 81-56 ))/2 }}} 


{{{x = (-9 +- sqrt( 25 ))/2 }}} 


{{{x = (-9 +- 5 )/2 }}} 


solutions:


{{{x = (-9 +5 )/2 }}} 

{{{x = -4/2 }}}

{{{x = -2 }}}

or

{{{x = (-9 -5 )/2 }}} 

{{{x = -14/2 }}}

{{{x = -7 }}}


{{{ graph(600, 600, -10, 10, -10, 20, x^2+9x+14) }}}