Answer:
[tex]x = 10[/tex]
Step-by-step explanation:
[tex]\sqrt{x+6} =x-6\\[/tex]
square both sides:
[tex]\implies x+6=(x-6)^2[/tex]
Expand brackets:
[tex]\implies x+6=x^2-12x+36[/tex]
Collect and combine like terms:
[tex]\implies x^2-13x+30=0[/tex]
[tex]\implies (x-10)(x-3)=0[/tex]
[tex]\implies x=10, x=3[/tex]
Substitute values back into original equation:
[tex]x=10: \sqrt{10+6} =10-6 \implies 4 = 4 \ \ \checkmark[/tex]
[tex]x=3: \sqrt{3+6} =3-6 \implies 3 = -3 \ \ \textsf{incorrect!}[/tex]
Therefore, [tex]x=10[/tex] only
