Question

Page - 3
Find the value of x by formula method:

3x2 +18x + 6 = 0​

Answer 1

Answer:

x=-0.667

Step-by-step explanation:

3x2+18x+6=0

6+18x+6=0

12+18x=0

18x=-12

x=-12/18

x= -0.667

Answer 2

Answer:

Now the clever bit: Take the coefficient of x , which is 6 , divide by two, giving 3 , and finally square it giving 9

Add 9 to both sides of the equation :

On the right hand side we have :

-2 + 9 or, (-2/1)+(9/1)

The common denominator of the two fractions is 1 Adding (-2/1)+(9/1) gives 7/1

So adding to both sides we finally get :

x2+6x+9 = 7

Adding 9 has completed the left hand side into a perfect square :

x2+6x+9 =

(x+3) • (x+3) =

(x+3)2

Things which are equal to the same thing are also equal to one another. Since

x2+6x+9 = 7 and

x2+6x+9 = (x+3)2

then, according to the law of transitivity,

(x+3)2 = 7

We'll refer to this Equation as Eq. #4.3.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

(x+3)2 is

(x+3)2/2 =

(x+3)1 =

x+3

Now, applying the Square Root Principle to Eq. #4.3.1 we get:

x+3 = √ 7

Subtract 3 from both sides to obtain:

x = -3 + √ 7

Since a square root has two values, one positive and the other negative

x2 + 6x + 2 = 0

has two solutions:

x = -3 + √ 7

or

x = -3 - √ 7