Step-by-step explanation:
Given,
[tex] \sqrt{x + 11} - x = - 1[/tex]
To Find:
Solution:
Square both sides, then solve.
[tex] \rm \implies \: \: \sqrt{(x + 11} ) {}^{2} = ( - 1 + x) {}^{2} [/tex]
[tex] \implies \rm \: x + 11 = - (1 + x) {}^{2} [/tex]
[tex] \rm \implies \: \: x + 11 = 1 - 2x + x {}^{2} [/tex]
[tex] \rm \implies \: 1−2x+x {}^{2}=x+11[/tex]
[tex] \rm \implies1+x {}^{2} −3x=11[/tex]
[tex] \rm \implies1+x {}^{2} −3x−11=0[/tex]
[tex] \rm \implies {x}^{2} - 3x - 10 = 0[/tex]
Factor the LHS
[tex] \implies \rm \: (x - 5)(x + 2) = 0[/tex]
Bring terms equal to 0, that is
[tex] \implies \rm(x - 5) = 0[/tex]
[tex] \implies \rm \: x = 5+ 0 = \boxed 5[/tex]
AND set x+2 equal to 0,
[tex] \rm\implies \: x + 2 = 0[/tex]
[tex] \rm \implies \: x = - 2[/tex]
So the possible two values are 5 & -2.
But, after plugging the values for verifying each,the most accurate is 5.
So, the value of x is 5.
