Question

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

square root of the quantity x plus 7 end quantity minus 1 equals x

Answer 1

x=2 true solution

x=-3 extraneous

Explanation:

sqrt(x+7) -1 = x

Add 1 to each side

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

sqrt(x+7) = x+1

Square each side

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

x+7 = x^2 +2x+1

Subtract x from each side

7 = x^2 +x +1

Subtract 7 from each side

0 = x^2 +x - 6

Factor

0 = (x+3)(x-2)

Using the zero product property

x+3 = 0 x-2 =0

x=-3 x=2

Check solutions

x=-3

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

sqrt(4) -1 = -3

3 =-3 extraneous

x=2

sqrt(2+7) -1 = 2

sqrt(9) -1 = 2

3 -1 =2

2 =2 true