find the factorization.
x2-75x-4
Answers
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:
Step-by-step explanation:
2x-75x-4
600