completing the square

[proven ice]

can someone please like explain how this is the method

[languid nest]

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[wild birch]

The formula for square of sum/difference is a^2 ± 2ab + b^2 = (a ± b)^2.
We look at the quadratic and linear terms: x^2 - 4x. We do the following:
x^2 - 4x = x^2 - 2*2*x
So, according to the formula above, what should the constant term be?

[proven ice]

oh ok wait i get this

but what about this question i dont know how he got 20 multiplied by 2

why did he multiply 20 by 2 why not multiply 40 by 5 because it says 5ax

and ax is 40 x

[wild birch]

Well, for (x + 20)^2 we just use the square of sum formula:
(x + 20)^2 = x^2 + 2(x)(20) + 20^2 = x^2 + 40x + 400
After that, we compare the coefficients on both sides.

[proven ice]

why arent you including the 3a is that js bc it isnt involved

where did u also get the 2(x)(20) +20^2 +40x + 400 from?

soz im a bit slow 😭

[wild birch]

Well, for now, I just showed what happens with (x + 20)^2. Of course, as (x + 20)^2 = x^2 + 40x + 400, then (x + 20)^2 - 3a = x^2 + 40x + 400 - 3a.

[wild birch]

From the square of sum formula.

[proven ice]

ohhh i get thisss

but i still dont see where the 2 is from

2 multiplied by 20

[proven ice]

whats that i thought u js had to complete the square

why wouldnt it be multiplied by 5

[wild birch]

Well, again, because (a + b)^2 = a^2 + 2ab + b^2, not a^2 + ab + b^2.