Question

Q:-
$2 {x}^{2} - 27$

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Answer 1

Answer:

Step by Step Solution:

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Step by step solution :

STEP

1

:

Equation at the end of step 1

2x2 - 27 = 0

STEP

2

:

Trying to factor as a Difference of Squares

2.1 Factoring: 2x2-27

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 2 is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Equation at the end of step

2

:

2x2 - 27 = 0

STEP

3

:

Solving a Single Variable Equation

3.1 Solve : 2x2-27 = 0

Add 27 to both sides of the equation :

2x2 = 27

Divide both sides of the equation by 2:

x2 = 27/2 = 13.500

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:

x = ± √ 27/2

The equation has two real solutions

These solutions are x = ±√ 13.500 = ± 3.67423

Two solutions were found :

x = ±√ 13.500 = ± 3.67423

Answer 2

Answer:

Given,

Area of rectangle = 25x2 – 35x + 12

We know, area of rectangle = length × breadth

So, by factoring 25x2 – 35x + 12, the length and breadth can be obtained.

25x2 – 35x + 12 = 25x2 – 15x – 20x + 12

=> 25x2 – 35x + 12 = 5x(5x – 3) – 4(5x – 3)

=> 25x2 – 35x + 12 = (5x – 3)(5x – 4)

So, the length and breadth are (5x – 3)(5x – 4).

Now, perimeter = 2(length + breadth)

So, perimeter of the rectangle = 2[(5x – 3)+(5x – 4)]

= 2(5x – 3 + 5x – 4) = 2(10x – 7) = 20x – 14

So, the perimeter = 20x – 14