# What is the value of $a$ in this equation?

I am new to this forum. And hoping to get some answers on some mathematical equations. Here is my first one -

$$(x - 5) (a + x) = x^2 - 25$$

What is the value of $$a$$ in this equation?

EDIT: This question is actually a multiple choice question from our BCS exam in the early 90's. And it actually had 4 options to answer as followed:

1) 5

2) -5

3) 25

4) -25

I also believe that the expression has a mistake and I actually cannot figure out the real problem. That's why I posted here, if anyone can figure that out. Hope this helps to all of you.

Please help me out. TIA.

Imran

Second edit: I have fixed the expression with correct equation value (replacing a with x). And also I have solved the math. Thanks for the all the suggestions.

• Do you want to solve this equation for $x$: $$0=x^2+5x-ax-a^2-5a-25$$? – Dr. Sonnhard Graubner Feb 9 at 13:45
• and $a$ is the given parameter – Dr. Sonnhard Graubner Feb 9 at 13:45
• Welcome to stackexchange. Your question is not clear. The equation has two variables, $a$ and $x$, so there is no "value of $a$". Perhaps you want to know $a$ in terms of $x$, or the opposite. Please edit the question to tell us just what you are asking, and show us what you tried and where you are stuck. (Don't put that in a comment - edit the question.) – Ethan Bolker Feb 9 at 13:47
• Do you require $x,a$ to be integers? – almagest Feb 9 at 19:33
• I edited my answer to reflect the edits that you made. – Michael Rybkin Feb 25 at 14:49

## 2 Answers

To solve for a in the equation $$(a - 5)(a + x) = x^2 - 25$$ expand the product, bring everything to the left side
and rewrite it as a quadradic equation in a.

This is a very simple question. Do you know what the difference of squares is? Here's what it looks like:

$$(x-y)(x+y)=x^2-y^2$$

$$25$$ is $$5^2$$ and $$a+x$$ is the same thing as $$x+a$$ by something called the commutative property of addition:

$$(x - 5) (a + x) = x^2 - 25\Longleftrightarrow (x - 5) (x+a) = x^2 - 5^2$$

It's quite clear from the above that $$a$$ should be $$5$$. So, the correct answer is $$1)$$.