Question

find the factorization.
x2-75x-4
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Answer 1

Step-by-step explanation:

Add 4 to both side of the equation :

x2+75x = 4

Now the clever bit: Take the coefficient of x , which is 75 , divide by two, giving 75/2 , and finally square it giving 5625/4

Add 5625/4 to both sides of the equation :

On the right hand side we have :

4 + 5625/4 or, (4/1)+(5625/4)

The common denominator of the two fractions is 4 Adding (16/4)+(5625/4) gives 5641/4

So adding to both sides we finally get :

x2+75x+(5625/4) = 5641/4

Adding 5625/4 has completed the left hand side into a perfect square :

x2+75x+(5625/4) =

(x+(75/2)) • (x+(75/2)) =

(x+(75/2))2

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

x2+75x+(5625/4) = 5641/4 and

x2+75x+(5625/4) = (x+(75/2))2

then, according to the law of transitivity,

(x+(75/2))2 = 5641/4

We'll refer to this Equation as Eq. #2.2.1

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

Note that the square root of

(x+(75/2))2 is

(x+(75/2))2/2 =

(x+(75/2))1 =

x+(75/2)

Now, applying the Square Root Principle to Eq. #2.2.1 we get:

x+(75/2) = √ 5641/4

Subtract 75/2 from both sides to obtain:

x = -75/2 + √ 5641/4

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

x2 + 75x - 4 = 0

has two solutions:

x = -75/2 + √ 5641/4

or

x = -75/2 - √ 5641/4

Note that √ 5641/4 can be written as

√ 5641 / √ 4 which is √ 5641 / 2

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Answer 2

Answer:

Step-by-step explanation:

2x-75x-4

600