X^2 + 5x + 25/4 is a perfect square trinomial?

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The discussion revolves around determining the missing number in the expression x^2 + 5x + __ to make it a perfect square trinomial. The correct answer is 25/4, derived from recognizing that (5/2)^2 equals 25/4. The user initially struggled with the concept but later realized that taking half of 5 and squaring it leads to the solution. This highlights the importance of understanding how to convert a quadratic equation into its perfect square form. The conversation emphasizes the learning process in pre-calculus and the significance of grasping foundational concepts.
EricPowell
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In my pre-calculus math class right now we are learning how to convert the standard form of a quadratic equation to general form. There are just some questions that are about filling in the missing number to make the equation, what I assume to be, a perfect square trinomial. Is that what the question is asking?

The textbook gives the answer as being 25/4. I have no idea how I would go about accomplishing that.

Homework Statement



2) Find a number that makes the expression a perfect square of the form (x+h)^2.

e) x2 + 5x + __



The Attempt at a Solution


I would think that I would have to find a perfect square whose root adds to 5 when multiplied by two. And I can not think of any such number.
 
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EricPowell said:
In my pre-calculus math class right now we are learning how to convert the standard form of a quadratic equation to general form. There are just some questions that are about filling in the missing number to make the equation, what I assume to be, a perfect square trinomial. Is that what the question is asking?

The textbook gives the answer as being 25/4. I have no idea how I would go about accomplishing that.

Homework Statement



2) Find a number that makes the expression a perfect square of the form (x+h)^2.

e) x2 + 5x + __

The Attempt at a Solution


I would think that I would have to find a perfect square whose root adds to 5 when multiplied by two. And I can not think of any such number.
Hello EricPowell. Welcome to PF !

Where did you get the 25/4 that's in the title of this thread?
 
NEVERMIND
Well now I feel silly...I never thought of thinking of 5/2 as being half of 5. 5/22 is 25/4.


Thank you for your efforts to help me though!
 
EricPowell said:
NEVERMIND
Well now I feel silly...I never thought of thinking of 5/2 as being half of 5. 5/22 is 25/4.


Thank you for your efforts to help me though!

And you want to write that as (5/2)2, not 5/22, which is equal to 5/4.
 

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