Question Solve for all values of x: sqrt (x)-5=sqrt (x+10) Answer Attempt 1out of 2 x=

Question

Answer 1

To solve the equation

, we can start by isolating one of the square roots.First, let's isolate

by adding 5 to both sides of the equation:

Next, we can square both sides of the equation to eliminate the square roots:

Simplifying the right side of the equation, we get:

Now, let's isolate the square root term by subtracting

from both sides:

Simplifying further, we have:

Next, let's isolate the square root term by subtracting 15 from both sides:

Simplifying, we get:

Now, let's isolate the square root term by adding

to both sides:

Finally, let's isolate the square root term by dividing both sides by 10:

To solve for

, we can square both sides of the equation again:

Simplifying, we get:

Multiplying both sides by 100, we have:

Rearranging the terms, we get a quadratic equation:

We can solve this quadratic equation using the quadratic formula:

In this case,

,

, and

. Plugging these values into the quadratic formula, we get:

Simplifying further, we have:

Therefore, the solutions for

are:

or

So, the final answer is:

or

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