Question

factorise (2x) ^ 2 + 6x ^ 2 + (3/4) ^ 2​

Answer 1

Step-by-step explanation:

4x^2+6x^2+(9/16)

10x^2+9/16

Answer 2

Answer:

x =(3-√13)/2=-0.303

Step-by-step explanation:

(2x2 - 6x) - 2 = 0

2x2 - 6x - 2 = 2 • (x2 - 3x - 1)

The first term is, x2 its coefficient is 1 .

The middle term is, -3x its coefficient is -3 .

The last term, "the constant", is -1

Step-1 : Multiply the coefficient of the first term by the constant 1 • -1 = -1

Step-2 : Find two factors of -1 whose sum equals the coefficient of the middle term, which is -3 .

-1 + 1 = 0

2 • (x2 - 3x - 1) = 0

y = 1.0 * 1.50 * 1.50 - 3.0 * 1.50 - 1.0

or y = -3.250

Root plot for : y = x2-3x-1

Axis of Symmetry (dashed) {x}={ 1.50}

Vertex at {x,y} = { 1.50,-3.25}

x -Intercepts (Roots) :

Root 1 at {x,y} = {-0.30, 0.00}

Root 2 at {x,y} = { 3.30, 0.00}

Add 9/4 to both sides of the equation :

On the right hand side we have :

1 + 9/4 or, (1/1)+(9/4)

The common denominator of the two fractions is 4 Adding (4/4)+(9/4) gives 13/4

So adding to both sides we finally get :

x2-3x+(9/4) = 13/4

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) = 13/4 and

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

then, according to the law of transitivity,

(x-(3/2))2 = 13/4

x2 - 3x - 1 = 0

has two solutions:

x = 3/2 + √ 13/4

or

x = 3/2 - √ 13/4

Note that √ 13/4 can be written as

√ 13 / √ 4 which is √ 13 / 2

- B ± √ B2-4AC

x = ————————

2A

In our case, A = 1

B = -3

C = -1

Accordingly, B2 - 4AC =

9 - (-4) =

13

Applying the quadratic formula :

3 ± √ 13

x = —————

2

√ 13 , rounded to 4 decimal digits, is 3.6056

So now we are looking at:

x = ( 3 ± 3.606 ) / 2

Two real solutions:

x =(3+√13)/2= 3.303

or:

x =(3-√13)/2=-0.303