please help me

[latresa31s]

I am suppose to slove the equation by completing the squre;simplify my answer express any complex numbers using i notation

the problem is

x^2 - 8x = 7

I have read the rules but I can't understand them.

 

[Unco]

Look at x² - 8x for the moment.

When we complete the square, we halve the -8 to get -4 and write this as
(x - 4)²

Now, if we were to expand this we would get
x² - 8x + 16

So that +16 needs to be substracted or else (x - 4)² is going to be 16 greater than x² - 8x.

So we write x² - 8x = (x-4)² - 16.

Back to the original equation, we have
(x-4)² - 16 = 7

Can you take it from there?

 

[latresa31s]

I just don't get it . I don't Know what you did to get the (X-4)^2 from X^2-8x. I do apologize for not getting this work and stressing you guys. but this is to hard to do with no instructor to explain every step. thanks for the help anyway.
and I don't know what to do with the rest of the problem

 

[Unco]

For some quadratic x² + bx + c = 0,

to complete the square, focus on the x² + bx part: we always halve 'b' so we have

(x + (b/2))².

If you expand (x + (b/2))², you have
...(x + (b/2))(x + (b/2)) = x² + x(b/2) +x(b/2) + (b²/²) = x² + b²/4.

This is something you will get used to with practise.

The next step is to subtract the b²/4 term which appears here because we only had x² + bx.

The 'c' term finally comes into play with simplification, after having completed the square.

If there was an 'a' infront of x² then there's little bit more work to do.

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