Question 669245
1.

{{{sqrt(6)-8=x}}}....move {{{8}}} to the right


{{{sqrt(6)=x+8}}}....both sides raise to the power of two

{{{(sqrt(6))^2=(x+8)^2}}}

{{{6=x^2+16x+64}}}

{{{0=x^2+16x+64-6}}}

or

{{{x^2+16x+58=0}}}.....use quadratic formula


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 


{{{x = (-16 +- sqrt( 16^2-4*1*58 ))/(2*1) }}} 


{{{x = (-16 +- sqrt( 256-232 ))/2 }}} 


{{{x = (-16 +- sqrt( 24 ))/2 }}} 


{{{x = (-16 +- 4.899)/2 }}}


solutions:

{{{x = (-16 + 4.899)/2 }}}


{{{x = (-11.101)/2 }}}


{{{highlight(x = -5.55) }}}

or


{{{x = (-16 - 4.899)/2 }}}


{{{x = (-20.899)/2 }}}


{{{highlight(x = -10.45) }}}


graph:

{{{ graph( 600, 200, -20, 5, -15, 75, x^2+16x+58) }}}


2.

{{{3sqrt(3x)-1=2}}}....move {{{-1}}} to the right

{{{3sqrt(3x)=2+1}}}

{{{3sqrt(3x)=3}}}....both sides raise to the power of two

{{{(3sqrt(3x))^2=3^2}}}

{{{9(3x)=9}}}

{{{3x=9/9}}}

{{{3x=1}}}

{{{highlight(x=1/3)}}}.........graph of a line that passes through the point 

({{{1/3}}},{{{0}}}) 

{{{ graph( 600, 200, -5, 5, -15, 15, 3sqrt(3x)-3) }}}


3.

{{{2sqrt(x+2)-3=7}}}....move {{{-3}}} to the right


{{{2sqrt(x+2)=7+3}}}


{{{2sqrt(x+2)=10}}}....both sides raise to the power of two


{{{(2sqrt(x+2))^2=10^2}}}


{{{4(x+2)=100}}}

{{{4x+8=100}}}

{{{4x=100-8}}}

{{{4x=92}}}

{{{x=92/4}}}

{{{highlight(x=23)}}}........graph of a line that passes through the point 

({{{23}}},{{{0}}}) 



{{{ graph( 600, 200, -15, 30, -15, 15, 2sqrt(x+2)-10) }}}