Question 404411
{{{sqrt(5x+21) = x + 3}}}.......to the second power


{{{(sqrt(5x+21))^2 = (x + 3)^2}}}

{{{5x+21 = x^2 + 6x + 9}}}


{{{0 = x^2 + 6x - 5x -21+ 9}}}...or

{{{x^2 + 6x - 5x -21+ 9 = 0}}}

{{{x^2 + x  -12 = 0}}}.....use quadratic formula and plug in {{{a=1}}},{{{ 

b=1}}}, and {{{c=-12}}}


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


{{{x = (-1 +- sqrt( 1^2-4*1*(-12) ))/(2*1) }}}


{{{x = (-1 +- sqrt( 1 + 48 ))/2 }}}


{{{x = (-1 +- sqrt( 49 ))/2 }}}

{{{x = (-1 +-  7 )/2 }}}


{{{x1 = (-1 + 7 )/2 }}}

{{{x1 = 6 /2 }}}

{{{x1 = 3 }}}


{{{x2 = (-1 -7 )/2 }}}

{{{x2 = (-8 )/2 }}}

{{{x2 = -4 }}}



check:

{{{sqrt(5x+21) = x + 3}}}........plug in {{{x1 = 3 }}}


{{{sqrt(5*3+21) = 3 + 3}}}


{{{sqrt(15+21) = 6}}}

{{{sqrt(36) = 6}}}

{{{6 = 6}}}