Question

2x^2+6x+9=0 complete the square​

Answer 1

Step-by-step explanation:

Solving 2x2-6x+9 = 0 by Completing The Square .

Divide both sides of the equation by 2 to have 1 as the coefficient of the first term :

x2-3x+(9/2) = 0

Subtract 9/2 from both side of the equation :

x2-3x = -9/2

Now the clever bit: Take the coefficient of x , which is 3 , divide by two, giving 3/2 , and finally square it giving 9/4

Add 9/4 to both sides of the equation :

On the right hand side we have :

-9/2 + 9/4 The common denominator of the two fractions is 4 Adding (-18/4)+(9/4) gives -9/4

So adding to both sides we finally get :

x2-3x+(9/4) = -9/4

Adding 9/4 has completed the left hand side into a perfect square :

x2-3x+(9/4) =

(x-(3/2)) • (x-(3/2)) =

(x-(3/2))2

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

x2-3x+(9/4) = -9/4 and

x2-3x+(9/4) = (x-(3/2))2

then, according to the law of transitivity,

(x-(3/2))2 = -9/4

We'll refer to this Equation as Eq. #3.2.1

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))2 is

(x-(3/2))2/2 =

(x-(3/2))1 =

x-(3/2)

Now, applying the Square Root Principle to Eq. #3.2.1 we get:

x-(3/2) = √ -9/4

Add 3/2 to both sides to obtain:

x = 3/2 + √ -9/4

In Math, i is called the imaginary unit. It satisfies i2 =-1. Both i and -i are the square roots of -1

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

x2 - 3x + (9/2) = 0

has two solutions:

x = 3/2 + √ 9/4 • i

or

x = 3/2 - √ 9/4 • i

Note that √ 9/4 can be written as

√ 9 / √ 4 which is 3 / 2