## lizzy87 3 years ago How to solve X^2+10x=24 by completing the square.

1. earslan100

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

2. earslan100

12 and -2 right?

3. znimon

or 4 and 6

4. henpen

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

5. earslan100

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

6. earslan100

srry it has to multiply to -24

7. henpen

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

8. henpen

*or her

9. earslan100

10. earslan100

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

11. henpen

Really, that's not completing the square.

12. henpen

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

13. earslan100

okie

14. earslan100

ur right srry

15. henpen

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

16. lizzy87

how didi you get the 5?

17. henpen

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

18. henpen

|dw:1346521508364:dw|

19. henpen

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

20. henpen

|dw:1346521563679:dw|

21. lizzy87

oh ok see how you got that thanks

22. henpen

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

23. henpen

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

24. henpen

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

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