A number squared + 1 is 26, what’s the number? Many think they did this RIGHT but will be WRONG!

How to solve a quadratic equation algebra word problem.

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[memyname]

While I got the accepted answer (your answer), the question was {a (one) number (singular) squared} + 1 = 26. Five is one single number that when squared equals 25. Minus five is another single number that when squared also equals 25. Based on the word problem, either answer would be totally correct. If the question was written as the formula x^2 +1 = 26, then your answer would be correct.

[michaelperine]

The question is "A" number squared plus 1 is 26. What is the number? "A" is the indefinite article and it is always singular. Therefore, either +5 or -5 solves the problem completely. Grammatically, you don't need both possible answers to be right. Math teacher gets a C in English!!!

[Ratel]

X^2+1=26

-This can be solved via brute force. Subtract 1 from 26 leaving you with 25.

X^2=25

-Take the square root of X^2 and 25.The square root of 25 =5

X=5

-"A number squared" is 5

5^2+1=26

[Kleermaker]

+/- 5 of course. sqr. rt of X^ = sqr. rt of 25, so X = +/-5 (we have to deal with a squared unknown, so two solutions).

[aryusure]

OK! You explained the rule. Got it! When you have 2 as the exponent in a quadratic equation there are 2 solutions.
But still you need to mess with the wording of the problem to make your point which can be considered misleading, no?
Personally I would use a more neutral formulation like this one:
If "n" squared 2 + 1 is 26, what's is the value of "n"?
The question "what is the number" is obviously tricky and the point is to understand and not to guess what the question means in fact.
Just saying!

[VR-ymys]

Good thing you are a math teacher and not an English teacher. You are asking for A number squared so either +5 or -5 is a completely correct answer. +/-5 is incorrect, because it is TWO numbers.

[armchairtin-kicker]

Algebraically speaking, because it is a quadratic equation, the highest power of the polynomial being two, there must be two solutions, real, imaginary, or the same. That stated, the second step is incorrect. It should have been...

sqrt(n^2)=±sqrt(25)

[davek]

You should expect 2 possible solutions to a quadratic equation.
It took you nearly 17 minutes to make that point. Are you being paid by the hour?
Or do you just need to create longer content to try and maximize your monetization?

[lamper]

50% was a solid F when I went to school and my teachers then weren't hesitant to give me that.

[thomastidswell]

I recall an early lesson by John that where the question is posited in positive terms then the answer is given only as a positive value.

[mingkee]

"a number" can be x
x² + 1 is 26
Move 1 to right side
x² is 26 - 1 >>> 25
x² is 25
x is √25
x is 5

[silverhammer]

"A number" implies that it can be either positive or negative, and since we're dealing with squares, it is definitely positive AND negative. N^2 + 1 = 26 => N^2 = 26 - 1 => N^2 = 25 => N = SQRT(25) = +/- 5.

[Geoff_G]

When you write ±5, it does not mean +5 AND -5, it means +5 OR -5.
But when you write it as +5, -5 then it means +5 AND -5.

[vanderpoolfarmsl.l.c.]

I love the daily problems but why the gaslighting in almost every title?
"Many think they did this RIGHT but will be WRONG!" "Many will fail" etc...
Not very encouraging or empowering.

[oldschoollew]

!/2 marks are exam stuff so getting 50% of 2 marks isnt bad on an exam, whereas 5 would give you a big X on a multiple choice test

[jessejames]

How do word games enhance the understanding of math?

[darkparker]

5.

And you asked for just one number. 5 and -5 are two numbers. So... 10/10 points.

[GryffieTube]

I honestly thought this was going to be a trick question otherwise I would have said + and - 5.

[MrMousley]

X squared + 1 = 26 so X squared = 26 - 1 = 25
The square root of 25 is 5 .. so X = 5
BUT because you say that most people will get this wrong
I'm going to say that the answer is 5 .. or - 5

[terry_willis]

If you use "x" instead of "n" do you still get full credit?