Question

Solve each equation by completing the square. if necessary found to the neares hundred.

Answer 1

x^2-x=2

Answer 2

@ganeshie8

Answer 3

take half of "x" coefficient

Answer 4

add its square both sides

Answer 5

ok so 1^2

Answer 6

what is "x" coefficient ?

Answer 7

1

Answer 8

whats half of 1 ?

Answer 9

1/2

Answer 10

\(\large x^2-x=2\)


\(\large x^2-2\times \frac{1}{2}x=2\)

Answer 11

so, add the missing \(\left(\frac{1}{2}\right)^2\) both sides, so that we can comlete the square

Answer 12

why is i t times

Answer 13

\(\large x^2-x=2 \)


\(\large x^2-2\times \frac{1}{2}x=2\)


\(\large x^2-2\times \frac{1}{2}x + \left(\frac{1}{2}\right)^2=2 + \left(\frac{1}{2}\right)^2\)

Answer 14

In the second step, I have just wrote 1 as 2*1/2

Answer 15

2*1/2 = 1,
so... nothing fishy ok ?

Answer 16

Next, look at the left hand side once,
does the pattern look familiar ?

Answer 17

\(\large a^2 - 2a b + b^2 \)

Answer 18

??

Answer 19

what

Answer 20

you should know this identity :

\(\large a^2 -2ab + b^2 = (a-b)^2 \)

Answer 21

the left hand side is exactly of above form,
so we can write it as a perfect square

Answer 22

\(\large x^2-x=2 \)


\(\large x^2-2\times \frac{1}{2}x=2\)


\(\large x^2-2\times \frac{1}{2}x + \left(\frac{1}{2}\right)^2=2 + \left(\frac{1}{2}\right)^2\)



rewriting the left hand side using a known identity : \(a^2-2ab+b^2 = (a-b)^2\)

\(\large \left( x - \frac{1}{2}\right)^2 =2 + \left(\frac{1}{2}\right)^2\)

simplifying the right hand side :

\(\large \left( x - \frac{1}{2}\right)^2 = \frac{9}{4}\)

Answer 23

take square root both sides

Answer 24

\(\large x^2-x=2 \)


\(\large x^2-2\times \frac{1}{2}x=2\)


\(\large x^2-2\times \frac{1}{2}x + \left(\frac{1}{2}\right)^2=2 + \left(\frac{1}{2}\right)^2\)



rewriting the left hand side using a known identity : \(a^2-2ab+b^2 = (a-b)^2\)

\(\large \left( x - \frac{1}{2}\right)^2 =2 + \left(\frac{1}{2}\right)^2\)

simplifying the right hand side :

\(\large \left( x - \frac{1}{2}\right)^2 = \frac{9}{4}\)

take square root both sides :

\(\large x - \frac{1}{2} = \pm \frac{3}{2}\)

Answer 25

you get : \(\large x = 2, -1\)

Answer 26

we're done. let me knw if somthng doesnt make sense