Solve the radical equation, and check all proposed solutions:

Question

anonymous · Answer

$$\sqrt{7x+44}=x$$

hero · Answer

Square both sides first. Let me know what you get afterwards.

anonymous · Answer

$$7x+44=x^{2}$$

hero · Answer

Subtract 7x from both sides. Then subtract 44 from both sides. Let me know what you get afterwards.

anonymous · Answer

$$0=x ^{2}-7x-44$$

hero · Answer

Split the middle term so that -7x = -11x + 4x

hero · Answer

$$0 = x^2 - 11x + 4x - 44$$

hero · Answer

Now factor by grouping

anonymous · Answer

(x-4)(x-11)?

hero · Answer

(x-4)(x-11) = 0

But you still have to solve for x

anonymous · Answer

how do I do that?

anonymous · Answer

Oh wait, it's (x+4)

hero · Answer

Yes, you're right

hero · Answer

x + 4 = 0
x - 11 = 0

Solve for x for both 

Only one x is the correct solution

anonymous · Answer

How would you find x for things like (5x+3)(5x+9)=0?

hero · Answer

Well, actually, both solutions work now that x = -4

hero · Answer

Again do the same thing

5x + 3 = 0
5x + 9 = 0

Solve for x

hero · Answer

Basically, you're applying what is called zero product property.

hero · Answer

`Zero Product Property
If the product of two numbers, a and b are zero, then a or b must equal zero:`


In other words, at least one of those numbers will be equal to zero.

anonymous · Answer

No, I got 4 not -4 so it didn't work

anonymous · Answer

What would be the domain of this equation?