Israel started to solve a radical equation in this way:

square root of x plus 6 βˆ’ 4 = x
square root of x plus 6 βˆ’ 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 βˆ’ 6 = x2 + 8x + 16 βˆ’ 6
x = x2 + 8x + 10
x βˆ’ x = x2 + 8x + 10 βˆ’ x
0 = x2 + 7x + 10
0 = (x + 2)(x + 5)

x + 2 = 0 x + 5 = 0
x + 2 βˆ’ 2 = 0 βˆ’ 2 x + 5 βˆ’ 5 = 0 βˆ’ 5
x = βˆ’2 x = βˆ’5

Solutions = βˆ’2, βˆ’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.

Q&A Education