Question 122489
{{{sqrt(7x+29) =x+3}}}...rise boyh sides to the 2 power

{{{(sqrt(7x+29))^2= (x+3)^2}}}...

{{{7x+29= (x+3)^2}}}...

{{{7x+29= x^2 + 6x + 9}}}...

{{{0 = x^2 + 6x -7x - 29 + 9}}}...

{{{ x^2 - x - 20 = 0}}}......use quadratis formula

{{{x[1,2] = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 

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


{{{x[1,2] = (1 +- sqrt( 1 + 80 ))/2 }}}

{{{x[1,2] = (1 +- sqrt(  81 ))/2 }}}

{{{x[1,2] = (1 +- (  9))/2 }}}


{{{x[1] = (1 + (  9))/2 }}}

{{{x[1] = 10/2 }}}

{{{x[1] = 5}}}


{{{x[2] = (1 - (  9))/2 }}}

{{{x[2] =  -(8)/2 }}}

{{{x[2] = - 4}}}


check:

{{{sqrt(7x + 29) =x+3}}}...plug in {{{x[1] = 5}}}

{{{sqrt(7(5)+29) = 5+3}}}...

{{{sqrt(35 + 29) = 8}}}...

{{{sqrt(64) = 8}}}...

{{{8 = 8}}}...
 

{{{sqrt(7x + 29) =x+3}}}...plug in {{{x[1] = -4}}}

{{{sqrt(7(-4)+29) = -4+3}}}...

{{{sqrt(-28 + 29) = -1}}}...

{{{sqrt(1) = -1}}}................since {{{sqrt(1)=(+1_or_-1)}}}, we can write

{{{-1= -1}}}...