## anonymous 3 years ago How to solve X^2+10x=24 by completing the square.

1. anonymous

what times what equals 24 and those same numbers have to add upto 10

2. anonymous

12 and -2 right?

3. anonymous

or 4 and 6

4. anonymous

$x^2+10x=(x+5)^2-25$ Do you understand this?

5. anonymous

no 4 and 6 when u multiply its 24 not -24

6. anonymous

srry it has to multiply to -24

7. anonymous

... or we could actually help him with the mechanics of the question

8. anonymous

*or her

9. anonymous

10. anonymous

if you multiply using foils u can see it equals the question

11. anonymous

Really, that's not completing the square.

12. anonymous

http://en.wikipedia.org/wiki/Completing_the_square Needs to be in the form (x+k)^2=c

13. anonymous

okie

14. anonymous

ur right srry

15. anonymous

Okay, @lizzy87 , do you understand why$x^2+10x=(x+5)^2-25$?

16. anonymous

how didi you get the 5?

17. anonymous

|dw:1346521462011:dw| Because 2x5=10

18. anonymous

|dw:1346521508364:dw|

19. anonymous

And if you take away 25 and cancel the 2 5x's into one 10x, that happens.

20. anonymous

|dw:1346521563679:dw|

21. anonymous

oh ok see how you got that thanks

22. anonymous

$x^2+10x=24$ $x^2+10x=(x+5)^2-25$ Therefore$24=(x+5)^2-25$ and$49=(x+5)^2$

23. anonymous

1- Did you understand that 2- What do you think we could do now to simplify?

24. anonymous

$\pm \sqrt{49}=x+5$