Question

Complete the steps in solving the quadratic function 7x – 9 = 7x2 – 49x by completing the square. –9 = 7x2 – x –9 + = 7(x2 – 8x + )

Answer 1

Answer:

A) 56 . . . . . . the (negative) sum of -7 and -49

b) 112 . . . . . the product of 7 and 16

c) 16 . . . . . . the square of 8/2

Answer 2

Answer:

x = 4 + (√ 103/7 )

  or

 x = 4 - (√ 103/7)

Step-by-step explanation:

7x – 9 = 7x2 – 49x

collect like terms, by brinin 7x2 – 49x to left hand side of the equation

  Solving   -7x^2+56x-9 = 0 by Completing The Square .

Multiply both sides of the equation by  (-1)  

7x^2-56x+9 = 0  Divide both sides of the equation by  7  to have 1 as the coefficient of the first term :

  x2-8x+(9/7) = 0

take away 9/7  from both side of the equation :

  x2-8x = -9/7

single out the coefficient of  x , which is  8 , divide by two, giving  4 , and finally square it to give  16  

Add  16  to both sides of the equation :

 On the right hand side we have :

  -9/7  +  16    or,  (-9/7)+(16/1)  

 The common denominator of the two fractions is  7   Adding  (-9/7)+(112/7)  gives  103/7  

 So adding to both sides we finally get :

  x2-8x+16 = 103/7

factorize the left hand side

  x2-8x+16  =

  (x-4) • (x-4)  =

 (x-4)2

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

  x2-8x+16 = 103/7 and

  x2-8x+16 = (x-4)^2

  (x-4)2 = 103/7

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

Note that the square root of

  (x-4)2   is

  (x-4)2/2 =

 (x-4)1 =

  x-4

Now, applying the Square Root Principle to  Eq. #4.2.1  we get:

  x-4 = +/-√ 103/7

Adding 4  to both sides to obtain:

  x = 4 +/- √ 103/7

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

  x2 - 8x + (9/7) = 0

  has two solutions:

 x = 4 + √ 103/7

  or

 x = 4 - √ 103/7

Note that  √ 103/7 can be written as

 √ 103  / √ 7