Finding for which value of $a$ are two equations equal(need instructions for method)

Question

I have the equations:

$(a - 5x)^2$

and

$25x^2 - 5x + a^2$

And I have a list of values for $a$ and for one of them, the two are equal. I just need to know what is the method for solving this - do I need to just plug in all the 4 possible answers or do I need to transform the equations somehow? I mean obviously I can't get the equations to be identical so is there any point in transforming them?

Answer 1

You want to find $a$ such that $(a-5x)^2 = 25x^2 - 5x + a^2$. Try expanding the term on the left-hand side of the equation, and see what happens.

Answer 2

Expand the left:

$25x^2-10ax+a^2=25x^2-5x+a^2$

Simplify:

$-10ax=-5x$

Simplify more:

$2a=1$

$a=\frac{1}{2}$