## anonymous one year ago Solve by completing the square x^2-20x+30=0

1. KaiserTheSlayer

using this would help you and remember the a=1, b=-20, and c=30

2. anonymous

$x^2-2*x*10+10^2-10^2+30=0$

3. anonymous

what do you do after that? @surjithayer

4. anonymous

do i used the quadratic formula to solve by completing squares? @KaiserTheSlayer

5. KaiserTheSlayer

yes

6. KaiserTheSlayer

so it would be x=18.36660026534076 and x= 1.63339973465925

7. anonymous

oh okay thank you

8. KaiserTheSlayer

yup

9. ChillOut

Solving by square completion yields:$x²-20x=-30$$x²-20x + 100 = 70$$(x-10)²=70$ There you have it. Do you the step-by-step?

10. anonymous

no i don't

11. anonymous

$(x-10)^2-100+30=0$ $\left( x-10 \right)^2=70=\left( \sqrt{70} \right)^2$ $x-10=\pm \sqrt{70}$ x=?

12. anonymous

where is the 100 coming from?

13. ChillOut

You take half of the x coefficient, square it and add to both sides.

14. anonymous

thats right! i sorta remember now

15. ChillOut

Don't forget to divide everything by whatever is multiplying the squared term ;). In this case, it's "1", so it won't matter.

16. anonymous

so then to figure out what x is I solve... x-10=$\sqrt{70}$ and x-10=$\sqrt{-70}$

17. anonymous

idk why it looks like that i was trying to write what you did on the last thing

18. ChillOut

Be careful! The second solution you gave is a COMPLEX number.

19. anonymous

i know i have to do the whole i stuff for that cause its a negative square root

20. ChillOut

No, it's not:$x-10=\sqrt{70}$or$x-10=-\sqrt{70}$

21. ChillOut

notice the minus sign is outside.

22. anonymous

yeah i see that now

23. ChillOut

And that's it! you have your solutions! Just move the independent term to the other side.

24. anonymous

yeah i got it now, thank you!

25. ChillOut

The whole thing about completing the square is to make the left side equation look like something like (x-a)² or (x+a)²