Question

Find the solution of 3 times the square root of the quantity of x plus 5 equals negative 9, and determine if it is an extraneous solution

Answer 1

Answer:

x = 4,  it is an extraneous solution.

Step-by-step explanation:

Translating the given statement, we get the following equation:

$3\sqrt{(x+5)} =-9$

Dividing both sides by 3, we get:

$\sqrt{(x+5)} =-3$

Now we will take square on both sides of the equation to get rid of the square root to get:

$(\sqrt{(x+5)} )^2=(-3)^2$

So we are left with:

$x+5=9\\\\x=9-5\\\\x=4$

Therefore, the solution is 4.

Also, it is an extraneous solution because the equality is not met by substituting x = 4 in the original equation:

$3\sqrt{(4+5)} =-9$

$3\sqrt{(9)} =-9$

$3(3) =-9$

$9\neq -9$