Question

Find the solution of 5 times the square root of the quantity of x plus 7 equals negative 10, and determine if it is an extraneous solution.

Answer 1

5sqrt(x+7)=-10
Dividing both sides by 5:
5sqrt(x+7)/5=-10/5
sqrt(x+7)=-2
Squaring both sides of the equation:
[sqrt(x+7)]^2=(-2)^2
x+7=4
x+7-7=4-7
x=-3

Replacing in the original equation:
5sqrt(x+7)=-10
5sqrt(-3+7)=-10
5sqrt(4)=-10
5(2)=-10
10=-10 It's not equal, then x=-3 is an extraneous solution