Help please a soon as possible

Please tell us what you have learned about quadratic equations, if anything, and what is the context of the question?
 
Pick any number for the 1st box and figure out what goes in the 2nd box.
 
In algebra (which you say this is), I would expect both squares to represent the same number. What were you told about the meaning of the problem?
 
If the two squares do not have to have the same value then there are infinitely many "correct' answers. Yes, \(\displaystyle 8^2- 2(5)= 64- 10= 54\) but it is also true that \(\displaystyle 2^2- 2(-25)= 4+ 50= 54\). If the two squares don't have to be the same then, as Jomo said, choose any number you like for the first square and you have a simple linear equation for the second square. If, for example, we choose the first square to be "4" then we have 16- 2[]= 54 so -2[]= 54- 16= 38. So the number in the second square is 38/-2= -19. Probably the two square are intended to be the same number. In more conventional terms the equation would be \(\displaystyle x^2- 2x= 54\). I would solve that by "completing the square, adding 1 to both sides: \(\displaystyle x^2- 2x+ 1= (x-1)^2= 55\). Then, taking the square root of both sides, \(\displaystyle x- 1= \pm\sqrt{55}\) so \(\displaystyle x= 1\pm\sqrt{55}\).
 
HallsofIvy said:
If the two squares do not have to have the same value then there are infinitely many "correct' answers. Yes, \(\displaystyle 8^2- 2(5)= 64- 10= 54\) but it is also true that \(\displaystyle 2^2- 2(-25)= 4+ 50= 54\). If the two squares don't have to be the same then, as Jomo said, choose any number you like for the first square and you have a simple linear equation for the second square. If, for example, we choose the first square to be "4" then we have 16- 2[]= 54 so -2[]= 54- 16= 38. So the number in the second square is 38/-2= -19. Probably the two square are intended to be the same number. In more conventional terms the equation would be \(\displaystyle x^2- 2x= 54\). I would solve that by "completing the square, adding 1 to both sides: \(\displaystyle x^2- 2x+ 1= (x-1)^2= 55\). Then, taking the square root of both sides, \(\displaystyle x- 1= \pm\sqrt{55}\) so \(\displaystyle x= 1\pm\sqrt{55}\).
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I have no intention to argue with anyone not Prof. Ivey in particular. But in my former life as a division chair, I forced into being "up on the state's standards" for mathematics at different grade levels. That said, beginning algebra is done as a middle school (say 7th or 8th grades). The standards that I have do not include quadratic equations. Now I am not naive enough to think that there is not a wide variation in standards. All I am saying is that we should respect what is commonly understood by beginning algebra. The original poster said in this thread that She/he did not know anything about quadratics.
 
pka said:
I have no intention to argue with anyone not Prof. Ivey in particular. But in my former life as a division chair, I forced into being "up on the state's standards" for mathematics at different grade levels. That said, beginning algebra is done as a middle school (say 7th or 8th grades). The standards that I have do not include quadratic equations. Now I am not naive enough to think that there is not a wide variation in standards. All I am saying is that we should respect what is commonly understood by beginning algebra. The original poster said in this thread that She/he did not know anything about quadratics.
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Like I said do you mean variable? If not please explained because I’m the person who doesn’t remember names or what things are called but once I see it I remember it.
 
We need information from you as to what you have been learning, in order to be positive what the question means. I think it's clear that the boxes are not meant to hold the same number, which means they do not represent a variable, but rather, at best, two different variables, and algebra is not really needed to solve it. But then, what were you told about its meaning, and what other things have you been learning that might shed light on its intent?

Note that many people put their questions under the wrong topic, so we can't depend on that fact that you called this "beginning algebra". Your questions have generally been at a level that could be pre-algebra.

In particular, if this is merely an exercise in trial and error to practice the order of operations, it seems inappropriate in even a beginning algebra class. (And it should not be implied that there is one correct answer.)

So, before we can tell you whether this is about variables, please tell us something about your class.
 
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