Divide both sides of the equation by 7 to have 1 as the coefficient of the first term :
x2-(2/7)x-(4/7) = 0
Add 4/7 to both side of the equation :
x2-(2/7)x = 4/7
Note: Take the coefficient of x , which is 2/7 , divide by two, giving 1/7 , and finally square it giving 1/49
Add 1/49 to both sides of the equation :
On the right hand side we have :
4/7 + 1/49 The common denominator of the two fractions is 49 Adding (28/49)+(1/49) gives 29/49
So adding to both sides we finally get :
x2-(2/7)x+(1/49) = 29/49
Adding 1/49 has completed the left hand side into a perfect square :
x2-(2/7)x+(1/49) =
(x-(1/7)) • (x-(1/7)) =
(x-(1/7))2
Things which are equal to the same thing are also equal to one another. Since
x2-(2/7)x+(1/49) = 29/49 and
x2-(2/7)x+(1/49) = (x-(1/7))2
then, according to the law of transitivity,
(x-(1/7))2 = 29/49
The Square Root Principle says that When two things are equal, their square roots are equal.
Now, applying the Square Root Principle, we get:
x-(1/7) = √ 29/49
Add 1/7 to both sides to obtain:
x = 1/7 + √ 29/49
Since a square root has two values, one positive and the other negative
x2 - (2/7)x - (4/7) = 0
has two solutions:
x = 1/7 + √ 29/49
or
x = 1/7 - √ 29/49
Note that √ 29/49 can be written as
√ 29 / √ 49 which is √ 29 / 7
I hope that helps
Take care
