Interesting radical equation | Can you solve ?

Added: 2026-05-09

[00:00:00]Hello, welcome back once again. Today we're going to solve this interesting radical equation. We have rootx + x is equal to 4. In this video, we're going to solve for the value of x that will satisfy this equation. Now let's carefully analyze this problem that is find out the domain of this equation.

[00:00:21]Now take this term here to the right hand side to get <unk>x is = 4 - x. Remember for the domain of this radical x must be greater than or equal to z which mean the left hand side is positive. Therefore the right hand side is as well positive telling us 4 - x is greater than or equal to zero.

[00:00:47]Right? And from here when you multiply both side by -1 we get x - 4 is less than or equal to 0. Add four to both side to see that x is less than or equal to 4. And you see what is going on here.

[00:01:04]We have x is greater than or equal to 0 and we have x is less than or equal to 4.

[00:01:11]So you can see that here is the best way to write the domain. 0 is less than or equal to x. yx is less than or equal to 4. Awesome.

[00:01:29]Okay. So from here to get rid of this radical let's square both sides of this equation. So we have roo<unk>x^² is = 4 - x² here square gets cancel with square root. Expand this binomial to get this term squared which is x 2 plus this 2 which is 16 - 2 * 4 * x which is 8 x. So this is equal to on the left hand side we're just left with oh my god that's just x right. So take this to the left hand side to get x^2 this is - 8 x then - x this is oh my god + 16 what's wrong with me? So + 16 is equal to 0. simplify properly to get x^2 which is a quadratic equation right - 9x + 16 is = 0.

[00:02:32]We're going to solve this using the general quadratic formula. So here we're going to have x= b in this case will be - 9 which is positive 9 plus or minus we have the square root of b ^ 2 b ^ 2 I mean is 9 2 which is 81us 4 * 1 * 16 giving us 64 from here and then divided by 2. So this will be equal to 9 plus or minus.

[00:03:02]Okay. So from here we got square root of so we're going to add I think 17.

[00:03:11]Yes. So we just have 17 here and then divided by 2. Now we know the domain of the equation is between 0 and 4.

[00:03:21]Obviously 9 + <unk>7 /2 falls out right.

[00:03:26]So x cannot be equal to 9 + 17 / 2. This one right over here is not a solution. It is xus. Now we can easily estimate the square root of 17 to be something around 4 something. And if you see 9 - 4 will give us 5, right? That is 9 - 17 is approximately equal to 5. When you divide this by 2, we get 2.5, which is between 0 and 4. So therefore, our solution here x is equal to 9 -<unk> 17 / 2. This one right over here is our valid solution. Thank you for watching.

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