what value of x satisfies the equation above?
x=

No Real Solutions

Step-by-step explanation:

So we have:

First, determine the domain restrictions. The expression under the radical cannot be less than 0. Therefore:

Therefore, our final answers must be greater than or equal to 3:

Now, going back to the original equation, subtract x from both sides:

Now, square both sides:

Distribute:

Subtract 4x and add 12 to both sides:

This isn't factor-able. Let's use the quadratic formula. a is 1, b is -4 and c is 12:

Substitute:

Simplify the radical:

The number under the radical is negative. In other words, there are no real solutions.

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8