## countonme123 3 years ago Solve quadratic equation by completing the square. Check both roots. problem below

1. countonme123

$2x^2-12x +16=0$

2. countonme123

please explain each step I am having trouble with it

3. Sonita

2(x^2-6x+8)=0 2[(x-4)(x-2)]=0

4. countonme123

please do explain why you do each step

5. NotTim

1st step- Factor out 2. Second step- What 2 numbers add to the end value, and multiply to the middle value?

6. NotTim

Those 2 values are then put into the brackets as you see them.

7. NotTim

And here, the signs of positive and negatives are reversed because when you solve for x individually, x-4=0 x=4. Ok?

8. countonme123

ok but there is supposed to be two answers

9. countonme123

4 is one of them

10. petewe

|dw:1339466532153:dw|

11. petewe

|dw:1339466562615:dw|

12. petewe

|dw:1339466604939:dw|

13. NotTim

eh, you might be might be making this more difficult than it actually is

14. petewe

I did what the question asked. Solve quadratic equation by completing the square.

15. NotTim

ay. missed that. thx.

16. KingGeorge

You made a small mistake. The -8 should also be multiplied by -2.

17. KingGeorge

Just 2 rather.

18. KingGeorge

Leaving you with$2(x^2-6x+9-9+8)=2((x-3)^2-1)=2(x-3)^2-2$

19. KingGeorge

Set equal to 0, and get $2(x-3)^2-2=0\implies(x-3)^2=1$Take the root, and solve. $x-3=\pm1\implies x=4\quad\text{or}\quad x=2$

20. countonme123

ok george you are right now can you explain each step

21. KingGeorge

The hardest part is the first couple steps. You start with $2x^2-12x+16=2(x^2-6x+8)$The next part is where you complete the square. You take half of $$-6$$, square it, and then add/subtract it. So you get$2(x^2-6x+8)=2(x^2-6x+\left(\frac{-6}{2}\right)^2-\left(\frac{-6}{2}\right)^2+8=2(x^2-6x+9-9+8)$

22. KingGeorge

Now you simplify as I described before. It's important that you simplify $x^2-6x+9-9+8$as $$(x-3)^2-1$$. That's the whole point of completing the square. You add/subtract just the right amount so you can have the square of a binomial. From there, you can solve for that square easily, and then just take a square root.

23. KingGeorge

Did this make sense?

24. countonme123

yes thank you but please view my next question