Question

Israel started to solve a radical equation in this way:

Square root of x plus 6 − 4 = x
Square root of x plus 6 − 4 + 4 = x + 4
Square root of x plus 6 = x + 4
(Square root of x plus 6)2 = (x + 4)2
x + 6 = x2 + 8x + 16
x + 6 − 6 = x2 + 8x + 16 − 6
x = x2 + 8x + 10
x − x = x2 + 8x + 10 − x
0 = x2 + 7x + 10
0 = (x + 2)(x + 5)

Answer 1

Israel started to solve a radical equation in this way:

Square root of x plus 6 − 4 = x
Square root of x plus 6 − 4 + 4 = x + 4
Square root of x plus 6 = x + 4
(Square root of x plus 6)2 = (x + 4)2
x + 6 = x2 + 8x + 16
x + 6 − 6 = x2 + 8x + 16 − 6
x = x2 + 8x + 10
x − x = x2 + 8x + 10 − x
0 = x2 + 7x + 10
0 = (x + 2)(x + 5)

x + 2 = 0 x + 5 = 0
x + 2 − 2 = 0 − 2 x + 5 − 5 = 0 − 5
x = −2 x = −5

Solutions = −2, −5

What error did Israel make?

He subtracted 6 before subtracting x.

He added 4 before squaring both sides.

He factored x2 + 7x + 10 incorrectly.

He did not check for extraneous solutions.

Answer 2

It is not B.

Answer 3

I think its A but not sure..I know he did C wrong but i just wanna see if he made a mistake in the early parts of it....I know he didn't get the right answer because the right answer is 2.

Answer 4

I know right?

Answer 5

He did not check for extraneous solutions.

Answer 6

Square root of x plus 6 − 4 = x

Answer 7

So, the answer is D, that he did not check for Extraneous solutions?