100x^2-20x+1=0 by completing the square method
Answers
Step-by-step explanation:
Divide both sides of the equation by 100 to have 1 as the coefficient of the first term :
x2-(1/5)x+(1/100) = 0
Subtract 1/100 from both side of the equation :
x2-(1/5)x = -1/100
Take the coefficient of x , which is 1/5 , divide by two, giving 1/10 , and finally square it giving 1/100
Add 1/100 to both sides of the equation :
On the right hand side we have :
-1/100 + 1/100 The common denominator of the two fractions is 100 Adding (-1/100)+(1/100) gives 0/100
So adding to both sides we finally get :
x2-(1/5)x+(1/100) = 0
Adding 1/100 has completed the left hand side into a perfect square :
x2-(1/5)x+(1/100) =
(x-(1/10)) • (x-(1/10)) =
(x-(1/10))2
Things which are equal to the same thing are also equal to one another. Since
x2-(1/5)x+(1/100) = 0 and
x2-(1/5)x+(1/100) = (x-(1/10))2
then, according to the law of transitivity,
(x-(1/10))2 = 0
Note that the square root of
(x-(1/10))2 is
(x-(1/10))2/2 =
(x-(1/10))1 =
x-(1/10)
Now, applying the Square Root Principle we get:
x-(1/10) = √ 0
Add 1/10 to both sides to obtain:
x = 1/10 + √ 0
The square root of zero is zero
This quadratic equation has one solution only. That's because adding zero is the same as subtracting zero.
The solution is:
x = 1/10
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