Question

o=24x2+168x+288 solve the factorization​

Answer 1

Answer:

Solving x2-24x-288 = 0 by Completing The Square .

Add 288 to both side of the equation :

x2-24x = 288

Now the clever bit: Take the coefficient of x , which is 24 , divide by two, giving 12 , and finally square it giving 144

Add 144 to both sides of the equation :

On the right hand side we have :

288 + 144 or, (288/1)+(144/1)

The common denominator of the two fractions is 1 Adding (288/1)+(144/1) gives 432/1

So adding to both sides we finally get :

x2-24x+144 = 432

Adding 144 has completed the left hand side into a perfect square :

x2-24x+144 =

(x-12) • (x-12) =

(x-12)2

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

x2-24x+144 = 432 and

x2-24x+144 = (x-12)2

then, according to the law of transitivity,

(x-12)2 = 432

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-12)2 is

(x-12)2/2 =

(x-12)1 =

x-12

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

x-12 = √ 432

Add 12 to both sides to obtain:

x = 12 + √ 432

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

x2 - 24x - 288 = 0

has two solutions:

x = 12 + √ 432

or

x = 12 - √ 432

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Answer 2

Answer:

24×2+168x+228 =444x solution