Question

solve :4x2-16x=15=0 by completing square method

Answer 1

Solving   4x2-16x-15 = 0 by Completing The Square .

 Divide both sides of the equation by  4  to have1 as the coefficient of the first term :
   x2-4x-(15/4) = 0

Add  15/4  to both side of the equation : 
   x2-4x = 15/4

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

Add  4  to both sides of the equation :
  On the right hand side we have :
   15/4  +  4    or,  (15/4)+(4/1) 
  The common denominator of the two fractions is  4   Adding  (15/4)+(16/4)  gives  31/4 
  So adding to both sides we finally get :
   x2-4x+4 = 31/4

Adding  4  has completed the left hand side into a perfect square :
   x2-4x+4  =
   (x-2) • (x-2)  =
  (x-2)2 
Things which are equal to the same thing are also equal to one another. Since
   x2-4x+4 = 31/4 and
   x2-4x+4 = (x-2)2 
then, according to the law of transitivity,
   (x-2)2 = 31/4

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

Note that the square root of
   (x-2)2   is
   (x-2)2/2 =
  (x-2)1 =
   x-2

Now, applying the Square Root Principle to  Eq. #3.2.1  we get:
   x-2 = √ 31/4 

Add  2  to both sides to obtain:
   x = 2 + √ 31/4 

Since a square root has two values, one positive and the other negative
   x2 - 4x - (15/4) = 0
   has two solutions:
  x = 2 + √ 31/4 
   or
  x = 2 - √ 31/4 

Note that  √ 31/4 can be written as
  √ 31  / √ 4   which is √ 31  / 2 

Answer 2

HELLO DEAR,


4x2 + 16x + -15 = 0 Reorder the terms: -15 + 16x + 4x2 = 0 Solving -15 + 16x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + 4x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 4x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 4x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 4x + x2 = 0 + 3.75 4x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 4x + x2 = 3.75 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 3.75 + 4 Reorder the terms: 4 + 4x + x2 = 3.75 + 4 Combine like terms: 3.75 + 4 = 7.75 4 + 4x + x2 = 7.75 Factor a perfect square on the left side: (x + 2)(x + 2) = 7.75 Calculate the square root of the right side: 2.783882181 Break this problem into two subproblems by setting (x + 2) equal to 2.783882181 and -2.783882181.

I HOPE ITS HELP YOU DEAR,
THANKS