in-3-38-solve-each-equation-for-the-variable-check-and-write-the-solution-set-sqrtx7

Question

In $3-38,$ solve each equation for the variable, check, and write the solution set.
$$
\sqrt{x}=7
$$

Martha Richards · Accepted Answer

So we&#x27;re asked to solve this equation for X, check it as well as provide the solutions that So when I have the radical ice later that can just square both sides and I get X on the left and seven square, it is a 49. So we&#x27;re gonna check this in the original equation squared of 49 is seven. So seven is equal to seven, so this checks out. So our solution set for these equation here is for X equal to 49.

Nick Johnson · Answer

one minus the cube root of X plus seven is equal to four. So first, let&#x27;s go ahead and subtract one from both sides. Equation that would give us negative. The cube root of X plus seven is equal to while four minus one, attracting one from both sides equally. Three. Okay, then let&#x27;s go ahead and just multiplied by a negative one to basically, we have a positive square room here. So if we do that, we get the square. The cube root excuse means to Cuba of X plus seven is gonna be then, while equal to negative three. So then, if we go ahead and cube both sides of the equation, right, the cube root of X plus seven cube just gives us experts seven. So eliminating the Q blue here. So we take the cube root of experts seven. And we cube it to just give us what&#x27;s under the cube root under the radical, which it&#x27;s just experts whips Whoops, which is just equal to X plus seven. Okay. And that&#x27;s gonna be that equal to negative three Cube. So you have negative three times negative three, which is a positive nine. But then times negative three, which is negative. 27 negative. Three Cube is gonna be equal to a negative 27. Okay. In the south for X, we just go ahead and we subtract seven from both sides of the equation. Right. Linear equation. Now. So therefore, experts 7 May 27. Then there. Four x is equal to negative 27 minus seven, which is equal to negative 34. So therefore, access equal to negative 34. Now, if we go ahead and we check negative 34 as a solution, does that work? While negative 34 plus seven is gonna be equal to negative 27. And the cube root of negative 27 is negative three. So we have one minus a negative. Groups one hopes one minus one minus and negative in negative. Three should be equal to four because one minus the cube root again off negative. 30 47 is negative. 27 in the cube root of native 27 is negative. Three So one minus. The native three is one plus three, which is for so we check out to get forwards equal before therefore, our solution is valid in our solution. Set here is the sets containing well, negative 34. All right, take care

Martha Richards · Answer

sore ass to solve this equation, check it and then provide the solution side. So we&#x27;ll start here. We have the radical isolated so I can square both sides and then I get a five. Plus a un left and seven squared is 49. So if I subtract five from both sides, I get the A is equal to a 44. So then plugging that back into the original equation I get here 44 plus five is the square root of 49 and then the square root of 49 is seven. So this does indeed check out in the solution set for this equation. Here, the square root by plus a sequel. The seven. It&#x27;s seven. Oh is sorry, 44.

Martha Richards · Answer

We&#x27;re gonna solve the solution here Checker answer and then provide the solution set for X. So here, when I have this cute, rude, isolated Aiken, just Q both sides. So then the left becomes X and two cubed is eight. So we&#x27;re gonna check her answer here. So when I put this back in the original equation, cubed root of eight is too. So this checks out. So our solution set for this equation here is for when acts is equal to eight.

Nick Johnson · Answer

Yes, we have the equation here. Five plus the square root of a is equal to seven. So first going to go ahead and subtract five from both sides. Gonna move All our numbers are constants toe one side of the equation to basically isolate a. So if we subtract five from both sides, we just get the square root of a is equal to seven minus five or squirt of a is equal to two. Now the software A. Since we have the square root of a, we could go ahead and square both sides. The square root of a squared is just equal toe a and then we get a is equal to out two squared just two times two So therefore a is equal to four. Meeting our solution set is the set containing four which would write just like that. All right, Victor

Nick Johnson · Answer

If you have the equation here, X is equal to the square root of four X plus five. So to go ahead and to basically eliminate the square root, go ahead and square both sides of the equation. So we just get well, X square is X squared, and that&#x27;s equal to the square root of four experts, I swear, which is just equal to what&#x27;s under the radical equal to four X plus five. Okay, so then we can go ahead and against you make this a quadratic in the standard form by sending this equal to zero. So subtract all our terms to the left side. We get that X squared minus four X and then minus five is equal to zero. Okay, so we have a quadratic equal to zero. We can try and go ahead and factor this and I believe this is gonna factor So we can&#x27;t this factors as well. X squared x Times X, not five. That&#x27;s five times one right. And then, well, we need a minus four x in the middle of self. A bit of minus on the five plus on the one that&#x27;s an X squared plus one x minus five X minus four X and then minus five times one minus five. Okay, that&#x27;s factored correctly. And that is that equal to zero. So we see here that X would be equal to either five or X would be equal to negative one. Okay, but let&#x27;s go ahead. And it&#x27;s actually check these solutions to make sure they actually work in our original equation here. So exited five. Well, then we have five is equal to the square root of four times five plus five. So we have five is equal to the square root of what times five is 20 plus five is 25. So we have five is equal to the square root of 25 which is true, right? Because the sport 25 is five. Therefore, we have five is equal to five. Check now, what about if access is a negative one? But then we have negative one is equal to four times negative. One plus five. Okay, so we&#x27;d have a negative one. Negative one is equal to the square root of of four times negative. One plus 54 times negative. One plus five. Okay. Would have negative one is equal to the square. Root off four times. Negative one is negative. Four plus five. Okay, we have negative. One is equal to while the square root of negative 4.5 is positive one. So we have one could have negative one is equal to the square. Root off one. Um well, right. The square root of one is one would have native one is equal toe one and do that is not true. Right? So therefore, our solutions that here is we have a vision, extraneous solution. Our solution sets would be just to set containing five so right that as a set containing the number first, right?

Problem

In $3-38,$ solve each equation for the variable, …

Problem 4 Easy Difficulty

In $3-38,$ solve each equation for the variable, check, and write the solution set.
$$
\sqrt{x}=7
$$

Answer

$\{49\}$

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$\{49\}$

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