Question 967588

{{{ sqrt( 5x+6 )= 2x-6 }}}

{{{ (sqrt( 5x+6 ))^2= (2x-6)^2 }}}

{{{ 5x+6 = (2x)^2-24x+6^2 }}}

{{{ 5x+6 = 4x^2-24x+36 }}}

{{{ 0 = 4x^2-24x-5x-6+36 }}}

{{{ 4x^2-29x+30=0 }}}...factor completely, write {{{-29x}}} as {{{-5x-24x}}}

{{{4x^2-5x-24x+30) = 0}}}...group

{{{(4x^2-5x)-(24x-30)) = 0}}}

{{{x(4x-5)-6(4x-5)) = 0}}}

{{{(x-6)(4x-5) = 0}}}

solutions:

if {{{(x-6) = 0}}}=>{{{x=6}}}

if {{{(4x-5) = 0}}}=>{{{4x=5}}}=>{{{x=5/4}}}


{{{ graph( 600, 600, -10, 10, -10, 50, (x-6)(4x-5)) }}}