Question

which term is added in X square + 6 X + 7 is equal to zero to make it complete square​

Answer 1

Step-by-step explanation:

Given: x

2

+6x−7=0

Now by using the identity (a+b)

2

=a

2

+2ab+b

2

Let us now compare the given equation to the identity and we see that,

a=x

and 2×a×b=6x

⇒2×x×b=6x(∵a=x)

∴b=

2x

6x

⇒b=3

⇒b

2

=9

Hence we can now complete the square for the above quadratic equation by adding 9 to both the sides

x

2

+6x−7+9=0+9

⇒x

2

+6x+9=9+7 ...{By transposing 7 to R.H.S}

⇒x

2

+6x+9=16

This can be written as

(x+3)

2

=(4)

2

∴x+3=±4 ....{Taking square root on both sides}

Now if,

x+3=4

⇒x=4−3

⇒x=1

or,

x+3=−4

⇒x=−4−3

⇒x=−7

∴ x=1 or −7 are the roots of x

2

+6x−7=0

I hope this answer is helpful for you