Question

Find the solution of 3 times the square root of the quantity of x plus 6 equals negative 12, and determine if it is an extraneous solution.

Answer 1

3 sqrt(x + 6) = -12
xqrt(x + 6) = -4

x + 6 = 16
x = 10

Substituting for x in the original equation:-

3 sqrt(10+6) = 3*sqrt16 = 3 * -4 = -12

not extraneous

Answer 2

You get an answer of x=10 from solving the equation, which is extraneous so there is no solution. see work attached