Question

solve. check for extraneous solutions

the square root of x + 8 equals x - 4

Answer 1

Square both sides.

Answer 2

how do i do that?

Answer 3

\[(\sqrt{x+8})^2=(x-4)^2\]

Answer 4

\[(\sqrt{x+8})(\sqrt{x+8})=(x-4)(x-4)\]

Answer 5

which would be x + 64 = x + 16?

Answer 6

No. On the left use this property:

Answer 7

\[(\sqrt{x})^2=x\]

Answer 8

On the right use this property:

Answer 9

\[(a-b)(a-b)=a^2-2ab+b^2\]

Answer 10

x^2 - 2x8 + 64?

Answer 11

x^2-8x+16

Answer 12

i don't understand, =/

Answer 13

\[(\sqrt{x+8})(\sqrt{x+8})=x+8\]

Answer 14

\[(x-4)(x-4)=x^2-4x-4x+16=x^2-8x+16\]

Answer 15

So now we have:
\[x^2-8x+16=x+8\]

Answer 16

Subtract x from both sides. Subtract 8 from both sides.

Answer 17

Then factor.