Question

Solve 3x 2 + 2 = 11 - x 2

Answer 1

You mean:
\[3x^2 + 2 = 11 - x^2\]

Answer 2

yes

Answer 3

Firstly add \(x^2\) both the sides first.. and tell me what did you get?

Answer 4

I dont know

Answer 5

Just add \(x^2\) will lead you to:
\[3x^2 + x^2 + 2 = 11 - x^2 + x^2\]

Can you solve here for Right Hand Side??

Answer 6

That would be 11

Answer 7

Yep:
And \(3x^2 + x^2 = ??\)

Answer 8

That's 0

Answer 9

I dont know I did it on the calculator

Answer 10

\(3x^2 + x^2\) = ??

Answer 11

Let \(x^2 = Banana\)..
See, if you have 3 bananas and I give you one more bananas then how many you have now???

Answer 12

thats 4

Answer 13

Yep, so \(4 \; bananas = 4x^2\)

Answer 14

yeah

Answer 15

So, now we have:
\[4x^2 + 2 = 11\]

Now subtract 2 from both the sides:
\[4x^2 + 2 - 2 = 11 - 2\]

Can you solve it further??

Answer 16

What will be left on LHS??

Answer 17

16x^2

Answer 18

2 -2 = ??

Answer 19

0

Answer 20

Yep:
and 11- 2 = ??

Answer 21

9

Answer 22

So you are left with:
\[4x^2 + \cancel{2} - \cancel{2} = 11 - 2 \implies 4x^2 = 9\]

Now divide by 4 here:
\[\frac{4x^2}{4} = \frac{9}{4}\]

Answer 23

In LHS, what will get cancelled??

Answer 24

4x^2

Answer 25

and 4 on the right

Answer 26

Only 4 will cancel out there:
\[\frac{\cancel{4}x^2}{\cancel{4}} = \frac{9}{4}\]

So you are left with:
\[x^2 = \frac{9}{4}\]

Take square root now and you will get:
\[\sqrt{x^2} = \sqrt{\frac{9}{4}}\]

And:
\[x = \sqrt{\frac{9}{4}}\]
Solve the RHS to find the answer..

Answer 27

What is \(\sqrt{9}\) = ??

Answer 28

And after that what is \(\sqrt{4}\) = ??

Answer 29

3 Thank You very much 2

Answer 30

SO:
\[\color{green}{x = \frac{3}{2}}\]

Answer 31

You are welcome dear..

Answer 32

You can add \(\pm\) in front of 3/2 if you want..