Solve by completing the square: x^2-8x+3

Question

anonymous · Answer

=(x^2 - 8x + 16) - 16 + 3
=(x - 4)(x - 4) - 13
=(x - 4)^2 - 13

anonymous · Answer

I don't get the first step

anonymous · Answer

okay. so what you have to do is look at just the the $$8x$$
what number adds together to make 8?
you want that number to be the same. so in this case, the number's 4, because 4+4 makes 8.

so then you get:
$$(x-4)(x-4)$$
but when you expand that, it's not the same as x^2 - 8x + 3. you get
$$x^2-8x+16$$
so what you have to do is subtract 16, since you can't just randomly add 16 to the original equation so that your factorizing can work. subtracting 16 as well basically means that you've added nothing to the original equation since 16-16 is 0. but it helps you factor out the $$(x-4)^2$$
so yeah. you subtract the 16. but don't forget about the 3 in your original equation. 
you have -16 +3, so you get -13.
so the overall answer is $$(x-4)^2-13$$

anonymous · Answer

Now to solve, you make that equation equal 0. :)

anonymous · Answer

i hope that makes sense.