## jazzyfa30 2 years ago Solve the equation by using the Square Root Property. x^2 = 10x + 24

1. jazzyfa30

@hartnn

2. hartnn

ok, so $$x^2-10x=24$$ the co-efficient of 'x' here is 10 divide it by 2 and square the result, what u get ?

3. hartnn

***the co-efficient of 'x' here is -10

4. jazzyfa30

so it would be x^2-5x=24

5. hartnn

no no.. the co-efficient of x is -10, right ? divide it by 2, you get -5, but then square it, $$\large (-5)^2=...?$$

6. jazzyfa30

2.23

7. jazzyfa30

is that right????

8. hartnn

umm...noo...how u got thta ?

9. jazzyfa30

i squared 5 isnt that what i was supposed to do

10. hartnn

5^2 =25

11. jazzyfa30

oh i thought i was supposed to square root it not square my b now what

12. hartnn

ohh...u took square root...we are supposed to square..

13. hartnn

ok, we add 25 on both sides $$x^2-10x+25=24+25$$ notice that left side is a perfect square! of ?

14. jazzyfa30

49

15. hartnn

49 is right side, and is the square of 7 what about left side ? x^2-10x+25 is squaree of ?

16. jazzyfa30

idk

17. hartnn

$$(x-5)^2 =... ?$$ can u find ?

18. jazzyfa30

x^2- 25

19. hartnn

nopes, $$(a+b)^2=a^2+2ab+b^2$$ so, $$(x-5)^2 =x^2-10x+25$$ so here we have $$(x-5)^2=7^2$$ take square root on both sides!

20. jazzyfa30

ok

21. jazzyfa30

then what

22. jazzyfa30

im confused

23. hartnn

did u take square root on both sides ? what u got ?

24. jazzyfa30

idk

25. hartnn

$$(x-5)^2=7^2 \implies x-5 = \pm 7 \\ x-5 =7 \quad \quad x-5=-7$$ get 2 values of 'x' from here!

26. jazzyfa30

but 7 isnt apart of any of my answer choices

27. hartnn

u need to solve x-5 =7 x-5 = -7

28. jazzyfa30

x= 12 x=-2

29. hartnn

correct!

30. jazzyfa30

ok Solve the equation by completing the square: x2 - 8x + 15 = 0

31. hartnn

same thing, here, the co-efficient of x is -8 divide it by 2, what u get ?

32. jazzyfa30

-4

33. hartnn

yes, then square it...what u get ?

34. jazzyfa30

-16

35. hartnn

-4 *-4 will be +16

36. jazzyfa30

oh

37. hartnn

so, adding 16 on both sides... $$x^2-8x+16=-15+16$$

38. jazzyfa30

right side:1 left side: idk

39. jazzyfa30

i think its x^2-4x-2x=1

40. jazzyfa30

is that right??????

41. jazzyfa30

42. hartnn

$$x^2-8x+16 = (x-4)^2$$ so, we have $$(x-4)^2=1$$ just take square root on both sides!

43. jazzyfa30

?????????

44. hartnn

when you take square root, the square part goes away! (x+4) =+1 or x-4 =-1 find 2 values of x from here...

45. jazzyfa30

(x-3)(x+3) i think

46. jazzyfa30

a. x = + 5 b. x =-3 or x = 5 c. x =3 or x = -5 d. x =3 or x =5

47. hartnn

x-4 = -1 , x = -1+4 = 3 is correct but for 2nd part, you get x-4 =1 x= 1+4 = 5

48. hartnn

so, 3,5

49. jazzyfa30

oh yea

50. jazzyfa30

Solve the equation by completing the square: x^2 + 2x = 120

51. terenzreignz

Do you know how to complete the square? :)

52. jazzyfa30

??????

53. terenzreignz

I see. Here's an example:$\Large x^2 + \color{red}6x =40$

54. terenzreignz

What you do is take that coefficient (number beside) the x with NO EXPONENT. In our case, 6.

55. terenzreignz

Take half of it, 3, and then square it, getting 9.

56. terenzreignz

Now, add that to BOTH SIDES of the equation. $\Large x^2 +\color{red}6x\color{blue}{+9}=40\color{blue}{+9}$

57. terenzreignz

Simplify. $\Large x^2+\color{red}6x+9=49$

58. terenzreignz

You'll notice that the left side is now what you call a 'perfect square trinomial' It may be expressed as... $\Large (x+\color{red}3)^2=49$

59. terenzreignz

Notice of course, that 3 is half of the original coefficient of x, which was 6. Now take the square root of both sides: $\Large \sqrt{(x+3)^2}=\sqrt{49}$ Notice that the square root and the square (exponent 2) cancel out. But the square root of 49 may be either positive or negative 7. $\Large x+3=\pm7$ Bring the 3 to the other side, you now get $\Large x = -3\pm7$ which means either x = -3 + 7 = 4 or x = -3 - 7 = -10 Case Closed :)

60. terenzreignz

So... go ahead now, get started with your own problem, using the same concepts. I'll walk you through it if you like :)

61. jazzyfa30

62. terenzreignz

63. jazzyfa30

u on skype or call me at 803-937-6271 cus by u typing it it is confusing m please

64. terenzreignz

I don't have skype. come on, we can do this... I'll get you started... $\Large x^2 +\color{red}2x = 120$

65. jazzyfa30

then call me i dont understand

66. jazzyfa30

@jessika96