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 minus 2 end quantity plus 8 equals x

Answer 1

x = 11.

Explanation:

√(x - 2) + 8 = x

√(x - 2) = x - 8

Square both sides:

x - 2 = x^2 - 16x + 64

x^2 - 17x + 66 = 0

(x - 6)(x - 11) = 0

x = 6, 11.

Test for an extraneous solution:

x = 6:

Left side = √(6-2) + 8 = 10

Right side = 6

x = 11:

Left side = √9 + 8 = 11

Right side = 11

So x = 6 is extraneous.