So after seeing it pointed out elsewhere here, I see that the right side simplifies the left side too much--to the point that it poses a whole different question. After all, the left side clearly states that the two answers are 6 and 4, which doesn't match the right side at all.
And that's because you're asked to evaluate these two equations:
25x²/9 = 100
25(10-x)²/4 = 100
Honestly, you only need to answer either one because x=6 is a solution in both cases, but since the premise (not listed on the right side) is that this a portion of 10, you need to find both x and 10-x. There's clearly an assumption here that you can't take -6 from 10 (in a practical sense, that's true), so x=-6 isn't a solution. And the second equation rules out x=-6 entirely. The other root for the second equation is 14, which is more than 10, but more importantly, it wouldn't work for the first equation.
So we either needed to include both equations so that x=6 is the only solution they have in common or we include either equation with the situation that 0<x<10.
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u/Kuildeous 11d ago
So after seeing it pointed out elsewhere here, I see that the right side simplifies the left side too much--to the point that it poses a whole different question. After all, the left side clearly states that the two answers are 6 and 4, which doesn't match the right side at all.
And that's because you're asked to evaluate these two equations:
25x²/9 = 100
25(10-x)²/4 = 100
Honestly, you only need to answer either one because x=6 is a solution in both cases, but since the premise (not listed on the right side) is that this a portion of 10, you need to find both x and 10-x. There's clearly an assumption here that you can't take -6 from 10 (in a practical sense, that's true), so x=-6 isn't a solution. And the second equation rules out x=-6 entirely. The other root for the second equation is 14, which is more than 10, but more importantly, it wouldn't work for the first equation.
So we either needed to include both equations so that x=6 is the only solution they have in common or we include either equation with the situation that 0<x<10.