Solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.

square root of the quantity x plus 6 end quantity minus 4 equals x

-2 is a real solution to the equation

-5 is extraneous (not a solution to the original)

Step-by-step explanation:

sqrt (x+6) - 4=x

Get square root thing by itself

Add 4 on both sides

sqrt (x+6) = x+4

Square both sides

x+6 = (x+4) ^2

x+6=x^2+8x+16

Subtract x and subtract 6 on both sides

0=x^2+7x+10

What two integers multiply to be 10 and add to be 7

Hope you said 2 and 5

0 = (x+2) (x+5)

x=-2 or x=-5

Check!

x=-2 gives:

sqrt (-2+6) - 4=-2

sqrt (4) - 4=-2

2-4=-2

-2=-2 true so x=-2 is good

Check!

x=-5 gives:

sqrt (-5+6) - 4=-5

sqrt (1) - 4=-5

1-4=-5

-3=-5 not true so x=-5 is bad