How do you solve by completing the square a2−6a−5=0?

2 Answers
Binayaka C.
Jun 8, 2018

Solution: a=3+√14anda=3−√14

Explanation:

a2−6a−5=0ora2−6a=5 or

a2−6a+9=5+9 or

(a−3)2=14ora−3=±√14 or

a=3±√14

Solution: a=3+√14anda=3−√14 [Ans]

Odlisss
Jun 8, 2018

a=3+√14,a=3−√14

Explanation:

When we want to make a square out of a quadratic polynomial, we need to look at the b-coefficient of the polynomial (assuming 0=ax2+bx+c).

We know that (a−b)2=a2−2ab−b2.
Therefore our "a" is just going to be a, and b is going to be some number for which :

−2ab=−6a
−2b=−6
b=3

So our square is going to be (a−3)2. However, the square equals to a2−6a+9 and we lack the +9 to complete the square.
Luckily, we are free to add a zero to the equation anytime we want. Like this :

a2−6a+(9−9)−5=0
a2−6a+9−9−5=0
(a−3)2−14=0
(a−3)2=14

Now we can square the equation, watch out for the plus/minus signs :

|a−3|=√14
a−3=±√14
a=3±√14

And we are finished.

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