Question

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

Answer 1

2 works

-3 is extraneous

Explanation:

sqrt(x + 7) - 1 = x Add 1 to both sides

sqrt(x + 7) = x + 1 Square both sides

(x + 7) = (x + 1 )^2

x + 7 = x^2 + 2x + 1 Subtract x from both sides

0 = x^2 + x + 1 -7

0 = x^2 + x - 6 This will factor

(x + 3)(x - 2) = 0 Find the values for x

x + 3 = 0

x = - 3

x - 2 = 0

x = 2

Now you must check this to see if both values work

sqrt(-3 + 7) - 1 = -3

sqrt(4) - 1 = -3

2 - 1 =? - 3

1 does not equal - 3. Therefore - 3 is extraneous. Try x = 2

sqrt(2 + 7) - 1 = 2

sqrt(9) - 1 = 2

3 - 1 = 2

2 = 2