Question 311736
{{{sqrt(x^2+2)=x+4}}}
Square both sides, (FOIL the right side
x^2 + 2 = x^2 + 8x + 16
:
combine the x's on the left
x^2 - x^2 - 8x = 16 - 2
:
-8x = 14
x = {{{14/(-8)}}}
x = -1.75
:
:
Check solution in original equation
{{{sqrt(-1.75^2+2)=-1.75+4}}}
{{{sqrt(3.0625+2)=2.25}}}
{{{sqrt(5.0625)=2.25}}}
2.25 = 2.25