Question 1123105

{{{sqrt(43 - x) = x - 1 }}}

{{{(sqrt(43 - x))^2 = (x - 1)^2 }}}

{{{43 - x = x^2 -2x+1 }}}

{{{0 = x^2+x -2x+1-43 }}}

{{{ x^2 -x-42=0 }}}

{{{ x^2+6x -7x-42=0 }}}

{{{ (x^2+6x )-(7x+42)=0 }}}

{{{ x(x+6 )-7(x+6)=0 }}}

{{{(x - 7) (x + 6) = 0}}}


solutions:

if {{{x - 7 = 0}}} =>{{{x=7}}}

if {{{ x + 6 = 0}}} =>{{{x=-6}}}


check:
{{{x=7}}}
{{{sqrt(43 - 7) = 7- 1 }}}=>{{{sqrt(36) = 6 }}}=>{{{6 = 6 }}} which is true

{{{x=-6}}}
{{{sqrt(43 - (-6)) =-6- 1 }}}=>{{{sqrt(49) = -7 }}}=>{{{7 = -7 }}} which is not true

so, your answer is C) {7}