Dentify all of the following solutions of square root of x plus 10 end root minus 4 equals x

Answers

x = - 6

x = - 1

x = - 6 and x = - 1

None of the above

x = - 1.

Step-by-step explanation:

√ (x + 10) - 4 = x

√ (x + 10) = x + 4

Squaring both sides:

x + 10 = x^2 + 8x + 16

x^2 + 8x - x + 6 = 0

x^2 + 7x + 6 = 0

(x + 6) (x + 1) = 0

x = - 6, - 1.

Check for any extraneous roots:

√ (x + 10) - 4 = x

Try x = - 6:

√ (-6 + 10) - 4 = 2 - 4 = - 2.

but we found x = - 6, so - 6 is not a root.

Try x = - 1:

√ (-1 + 10) - 4 = 3 - 4 = - 1. So x = - 1 is a root.

x=-1

Step-by-step explanation:

sqrt (x+10) - 4 = x

sqrt (x+10) = x+4

square each side

x+10 = (x+4) ^2

x+10 = x^2+8x+16

subtract x+10 from each side

x^2+7x+6=0

(x+6) (x+1) = 0

x=-6 x=-1

Then we plug both back into the equation.

sqrt (-1+10) - 4 = - 1

sqrt (9) - 4 = - 1

3-4 = - 1

-1=-1. this works out.

sqrt (-6+10) - 4 = - 6

sqrt (4) - 4 = - 6

2-4 = - 6

-2 = - 6. this does not work so the only solution is x=-1