Solving for X involving Square Roots

In summary, the conversation discusses solving an equation involving square roots and finding the value of x. The person is frustrated and asks for help, while also sharing their current understanding of the problem. Through the conversation, it is revealed that squaring both sides of the equation can help simplify it and ultimately lead to the solution of x=7.
  • #1
yoyo
21
0
Hi, I am getting frustrated with trying to solve this equation:

sqrt(x+9) - sqrt(x-6) = 3.

I know that the answer is x=7 because of guess and check. I don't know how to show it algebraically. Squaring both sides will cancel out the x. Is there a trick or something this? Please help. Thanks in advance.
 
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  • #2
Can you show how squaring both sides cancels out the x?

If I square both sides I get:

(sqrt(x+9) - sqrt (x-6))^2 = 3^2

x+9 - 2*sqrt(x+9)*sqrt(x-6) + x - 6 = 9

2x + 3 - 2*sqrt((x+9)(x-6)) = 9
...
 
  • #3
oh i see what you are saying. Silly mistake on me. Thank you so much!
 

FAQ: Solving for X involving Square Roots

How do you solve for x involving square roots?

To solve for x involving square roots, you need to isolate the square root expression on one side of the equation. Then, you can square both sides of the equation to eliminate the square root and solve for x.

What is the purpose of solving for x involving square roots?

Solving for x involving square roots is useful in solving equations in which x is under a square root, such as in quadratic equations. It allows us to find the value of x that satisfies the equation.

Can we solve for x involving square roots if there are multiple square root expressions?

Yes, we can still solve for x involving multiple square root expressions. The key is to isolate all the square root expressions on one side of the equation and then square both sides to eliminate them.

Are there any special rules for solving for x involving square roots?

Yes, there are a few rules to keep in mind when solving for x involving square roots. One important rule is to always check the solutions you get by plugging them back into the original equation to make sure they are valid.

Are there any alternative methods for solving for x involving square roots?

Yes, there are alternative methods for solving for x involving square roots, such as using the quadratic formula or factoring. These methods may be more efficient in certain cases, so it's important to know them as well.

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