What is the value of x? Round to the nearest tenth.

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What is the value of x? Round to the nearest tenth.

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\(\large\color{black}{ \displaystyle a^2+b^2=c^2 }\) where c is the hypotenuse of a right triangle, and a & b are the legs.
Would you then agree with the following set up (to find x)? \(\large\color{black}{ \displaystyle 12^2+x^2=22^2 }\)

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Yes
ok, then tell me what x is going to equal (and disregard the negative x solution)
10
no
it is not 12+x=22 then it would have been correct, BUT///
it is 12²+x²=22²
oh ok
first, you have to simplify the powers.
12²=? 22²=?
144
484
yes
\(\large\color{black}{ \displaystyle 12^2+x^2=22^2 }\) \(\large\color{black}{ \displaystyle 144+x^2=484 }\) when you subtract 144 from both sides, you get: \(\large\color{black}{ \displaystyle x^2=340 }\)
So, x² is 340
okay
then take the square root of both sides.
okay
then?
so what's the final answer? @SolomonZelman
@SolomonZelman i running out of time please
i'm*
\(\large\color{black}{ \displaystyle x^2=340 }\) \(\large\color{black}{ \displaystyle \sqrt{x^2}=\sqrt{340} }\) \(\large\color{black}{ \displaystyle x=\pm \sqrt{340} }\) exclude the negative result, as a side can't be negagive. \(\large\color{black}{ \displaystyle x=\sqrt{340} }\) \(\large\color{black}{ \displaystyle x=\sqrt{4\times 85} }\) \(\large\color{black}{ \displaystyle x=2\sqrt{85} }\)

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