SOLUTION: Solve the equation. Sqrt(x^2 - 24) = Sqrt(x + 6) I am lost on this one. I came up with no solution..not sure if its right.

Question 382368: Solve the equation.
Sqrt(x^2 - 24) = Sqrt(x + 6)
I am lost on this one.
I came up with no solution..not sure if its right.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

We need to get rid of the square roots so we can "get at" the variable. So we start by squaring both sides of the equation:

This simplifies to:

This is now a quadratic equation. So we want one side of the equation to be zero. Subtracting x and 6 from each side we get:

Now we factor (or use the Quadratic Formula). This factors pretty easily:
(x-6)(x+5) = 0
From the Zero Product Property we know that this (or any) product can be zero only if one (or more) of the factors is zero. So
x-6 = 0 or x+5 = 0
Solving these we get:
x = 6 or x = -5

Whenever you solve square root equations like yours, you square both sides of the equation. This is not wrong. But doing so can introduce what are called extraneous solutions. Extraneous solutions are solutions that work in the squared equation but do not work in the original equation. For this reason we must check our answers.

When checking answers use the original equation:

Checking x = 6:

Check!

Checking x = -5:

Check!

RELATED QUESTIONS
Solve by completing the square. x^2 -14x +49 = 0 I came up with the answer of 7, 7 for... (answered by checkley75)

Can someone help me with this i've tried and i am not ending up with the right solutions. (answered by tutorcecilia)

solve sqrt x + sqrt x-3 =0 im coming up with no solution am i right thank... (answered by Fombitz,ewatrrr)

I need help on this one: (x)/(x+5)-(5)/(x-5)=(x^(2)+25)/(x^(2)-25) I come up with no... (answered by Alan3354)

x2 + 24x + 144 I came up with this, not sure if im on the right track (X +12) * (x + (answered by london maths tutor)

I need to solve this radical equation using the power principle. Problem:... (answered by ankor@dixie-net.com)

I have a worksheet and have two questions for you. I am totally lost. 1. Solve... (answered by gonzo)

Solve and check equation for x. x/6 - x/8 = 1 This is what I have, but am not sure (answered by Earlsdon,MathLover1,stanbon)

Here is my question: 6 - sqrt of 20 -------------- = ????? 2 I came up... (answered by ptaylor)