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
