Question

x² + 10x = 18

Answer 1

Firstly subtract 18 from both the sides...

Answer 2

\[x ^{2}+10x-18\]

Answer 3

Or precisely we are to bring 18 to left hand side too, so can you do the subtraction by 18 both the sides??

Answer 4

After 18??

Answer 5

-18

Answer 6

That is not complete...

\[x^2 + 10x - 18 = 0\]

Answer 7

k

Answer 8

Here as there is no factorization possible, so we must go with Quadratic Formula..

Answer 9

can you tell me what are a, b and c here comparing it with:

\[ax^2 + bx + c = 0\]

Compare it with our equation and can you tell a, b and c values??

Answer 10

a= 1 b= 10 c= -18

Answer 11

Yep...

Good..

Now let us find Discriminant here..

\[D = b^2 - 4ac\]

can you plug in the values and find D here??

Answer 12

d=10^2-4(1)(-18)

Answer 13

=172

Answer 14

Yep..

So can you find here \(\sqrt{D}\) not in decimals but just reduce he radical..

Answer 15

so \[\sqrt{172}\]

Answer 16

\[\sqrt{D} = \sqrt{72}\]

Answer 17

*172..

Answer 18

y just 72?

Answer 19

But you have to reduce 172, can you do that??

Answer 20

nope

Answer 21

See for an example if D = 20 then how we will reduce it? Look below:

\[\sqrt{D} = \sqrt{20} \implies \sqrt{2 \times 2 \times 5} \implies 2 \sqrt{5}\]

Answer 22

Like this make factors of 172 and take out which you can take out of the square root brackets..

Answer 23

you just lost me

Answer 24

Oh sorry, so for a second assume that we are here:

\[\sqrt{D} = \sqrt{172}\]

Okay?

Answer 25

=13.1148

Answer 26

Don't calculate it buddy..

Answer 27

Just remember it:

Now use the formula:

\[x = \frac{-b \pm \sqrt{D}}{2a}\]

Can you use this?? Here : \(\sqrt{D} = \sqrt{172}\)

Answer 28

Just plug in the values..

Answer 29

\[\frac{ \[-10\pm \sqrt{172}\]}{ 2(1)}\]

Answer 30

Yep..

So let us now reduce 172 that is the only thing we are left with..

See can you make prime factors of 172 or not??

Answer 31

what do you mean by prime factors?

Answer 32

Like :

\[50\]

50 can be written as :

\[50 = 2 \times 5 \times 5\]

Right??

Answer 33

yea

Answer 34

Here 2 and 5 are nothing but prime numbers, so this is called Prime Factorization..

Answer 35

2*2*43

Answer 36

Very Good..

Answer 37

So:
\[\sqrt{D} = \sqrt{2 \times 2 \times 43} = ??\]

Answer 38

13.11

Answer 39

As per rules of square roots, you can take one 2 out of the brackets, right??

Answer 40

No buddy,

this is like:

\[\sqrt{D} = \sqrt{2 \times 2 \times 43} = 2 \sqrt{43} \qquad \quad Right??\]

Answer 41

yeah

Answer 42

Yep..

So now we have :

\[x = \frac{-10 \pm 2 \sqrt{43}}{2}\]

can you factor out 2 from numerator??

Answer 43

*2?

Answer 44

Yep...

Answer 45

Like this:

\[20 + 10 \implies 2(10 + 5)\]

Answer 46

so \[10\pm2\sqrt{43}\times2\] ?

Answer 47

See:

Factor out 2 means taking common like this:

\[x = \frac{- 5 \times 2 \pm 2 \sqrt{43}}{2} \implies \frac{2(-5 \pm \sqrt{43})}{2}\]

So that you can cancel 2 with below 2 now..

Getting??

Answer 48

1.56

Answer 49

It depends if you want to find x in decimal or without decimal..

\[x = -5 \pm \sqrt{43}\]

Answer 50

Here you will get two values of x:
One by solving this:
\[x = -5 + \sqrt{43}\]
and other by solving this:
\[x = -5 - \sqrt{43}\]