Solving x+x^1/2 = 6 - Can You Help?

[EngTechno]

I have got stuck with this simple problem,

x +x^1/2=6 ( x plus square root of x is equal to 6 )

Although I know the answer is 4, I don't know how to systmatically calculate this problem. Do you know? And how?

 

[Justin Lazear]

Let u = $\sqrt{x}$, and then you have a quadratic in u.

--J

 

[tacman]

Sure, I'd be happy to help you solve this problem! First, let's rewrite the equation as x +√x = 6 to make it a little easier to work with. Then, we can isolate the square root term by subtracting x from both sides:

√x = 6 - x

Next, we can square both sides to eliminate the square root:

(√x)^2 = (6 - x)^2

Simplifying, we get:

x = 36 - 12x + x^2

Now, we can rearrange the terms to get a quadratic equation in standard form:

x^2 - 13x + 36 = 0

This can be factored as (x - 9)(x - 4) = 0, which means that x can equal either 9 or 4. However, we need to check our solutions to make sure they work in the original equation. Plugging in x = 9 gives us 9 + √9 = 6, which is not true. But when we plug in x = 4, we get 4 + √4 = 6, which is true. Therefore, our solution is x = 4.

I hope this helps you understand the systematic approach to solving this problem. Keep practicing and you'll become more comfortable with solving equations like this!