## anonymous 4 years ago how do i solve x2 – 2x = 8 by completing the square?

1. anonymous

$(x-1)^2=8+1=9$ $x-1=\pm3$ $x-1=3\implies x=4$ $x-1=-3\implies x=-2$

2. anonymous

i need to show the work, can you explain how you got this?

3. anonymous

Could you @satelite try to answer my question

4. anonymous

Ummm

5. anonymous

We generally don't complete the square to solve for a variable. We usually use it to place a quadratic equation into vertex form in order to graph or solve a word problem. $x ^{2}-2x=8$ Bring everything to one side $x ^{2}-2x-8=0$ Now we place brackets around the first two terms: $(x ^{2}-2x)-8=0$ Now we need to create a nice perfect square in the brackets. We do this by taking half of x's coefficient and squaring it. In this case (2/2)^2 = 1 We then add and subtract this number, thereby not "really" changing the equation. $(x ^{2}-2x+1-1)-8=0$ We bring the subtracted term out of the brackets: $(x ^{2}-2x+1)-1-8=0$ Then we factor the bracket: $(x-1)^{2}-1-8=0$ Simplify: $(x-1)^{2}-9=0$ That would be vertex form (if the 0 was a y) So if we want to solve: $(x-1)^{2}=9$ Square root both sides, this actually gives us a plus and minus version: $x-1= +/-3$ so we have two solutions: $x=-2$ and $x=4$