1
00:00:00,998 --> 00:00:07,082
We're asked to solve the equation 2x squared plus 3 = 75.

2
00:00:07,082 --> 00:00:13,584
So in this situation looks like we might be able to isolate the x squared pretty simply. 'Cause

3
00:00:13,584 --> 00:00:15,733
there's only one term that involves an x here. It's the only

4
00:00:15,733 --> 00:00:19,064
x squared term. So lets try to do that. So let me just rewrite

5
00:00:19,064 --> 00:00:19,574
it.

6
00:00:19,574 --> 00:00:26,587
So 2x squared + 3 = 75. I'm going to try to isolate this x squared

7
00:00:26,587 --> 00:00:27,980
over here. The best way to do that

8
00:00:27,980 --> 00:00:29,420
or at least the first step, would

9
00:00:29,420 --> 00:00:32,067
be the subtract 3 from both sides of this equation.

10
00:00:32,067 --> 00:00:35,067
So lets subtract 3 from both sides.

11
00:00:35,067 --> 00:00:41,169
The left hand side we're just left with 2x squared. That was the whole point of subtracting 3 from both sides.

12
00:00:41,169 --> 00:00:45,720
And on the right hand side 75 minus 3 is 72.

13
00:00:45,720 --> 00:00:49,467
Now I wanna isolate this x squared, I have a 2x squared here.

14
00:00:49,467 --> 00:00:53,336
So I could have just have an x squared here if I divide

15
00:00:53,336 --> 00:00:53,836
this side

16
00:00:53,836 --> 00:00:54,336
or

17
00:00:54,336 --> 00:00:55,240
really both sides by 2. Anything that I do on 1 side,

18
00:00:55,240 --> 00:00:56,076
I have to do the other side.

19
00:00:56,076 --> 00:00:59,048
If I want them to mantain the quality.

20
00:00:59,048 --> 00:01:01,742
So the left side just becomes x squared.

21
00:01:01,742 --> 00:01:07,315
And the right hand side, the 72 divided by 2 is 36. So we're up with x

22
00:01:07,315 --> 00:01:07,965
squared

23
00:01:07,965 --> 00:01:08,465
is

24
00:01:08,465 --> 00:01:08,965
equal

25
00:01:08,965 --> 00:01:09,465
to

26
00:01:09,465 --> 00:01:09,965
36.

27
00:01:09,965 --> 00:01:14,420
And then to solve for x we can take the positive plus or minus

28
00:01:14,420 --> 00:01:18,042
squared root of both sides. So we can say the plus or

29
00:01:18,042 --> 00:01:19,668
let me right it this way.

30
00:01:19,668 --> 00:01:24,172
If we take the squared root of both sides, we would get x

31
00:01:24,172 --> 00:01:25,240
is

32
00:01:25,240 --> 00:01:25,751
equal

33
00:01:25,751 --> 00:01:26,401
to

34
00:01:26,401 --> 00:01:33,321
the plus or minus square root of 36. Which is equal to plus or minus

35
00:01:33,321 --> 00:01:33,971
6. let me just write it on another line.

36
00:01:33,971 --> 00:01:37,965
So x is equal to plus or minus 6.

37
00:01:37,965 --> 00:01:38,847
And remember here!

38
00:01:38,847 --> 00:01:42,748
If something squared is equal to 36, that something could be the negative

39
00:01:42,748 --> 00:01:43,909
version, or the positive version.

40
00:01:43,909 --> 00:01:46,649
It could be the principle root, or it could be the negative root.

41
00:01:46,649 --> 00:01:51,333
Both negative 6 squared is 36 and positive 6 squared is 36.

42
00:01:51,333 --> 00:01:54,498
So both of these work. And you can put them back into the original

43
00:01:54,498 --> 00:01:57,423
equation, to varify it. Let's do that. If you say

44
00:01:57,423 --> 00:02:03,414
2 times 6 squared plus 3, that's 2 times 36 which is 72

45
00:02:03,414 --> 00:02:05,968
plus 3 is 75. So that works.

46
00:02:05,968 --> 00:02:08,662
If you put negative 6 in there, you're going to get the exact same result.

47
00:02:08,662 --> 00:02:13,399
Cause negative 6 squared is also 36, 2 times 36 is 72,

48
00:02:13,399 --> 99:59:59,999
plus 3 is 75.