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5 votes
Complete the square: ax^2 + x + 3.

2 Answers

6 votes

Answer:


a(x+(1)/(2a))^2)-(1)/(4a)+3

Explanation:

We have been given an expression
ax^2+x+3. We are asked to complete the square for the given expression.

First of all, we will factor our a as:


a(x^2+(x)/(a))+3


a(x^2+(1)/(a)x)+3

Now, we need to add and subtract half the square of the middle term, that is
((1)/(2a))^2:


a[x^2+(1)/(a)x+((1)/(2a))^2-((1)/(2a))^2]+3


a[x^2+(1)/(a)x+((1)/(2a))^2-((1)/(4a^2))]+3


a(x^2+(1)/(a)x+((1)/(2a))^2)+3-a*(1)/(4a^2)


a(x+(1)/(2a))^2)-(1)/(4a)+3

Therefore, our required square would be
a(x+(1)/(2a))^2)-(1)/(4a)+3.

User Rudra Prasad Samal
by
8.3k points
3 votes

Answer:

The value of a is
(1)/(12).

Explanation:

The given expression is


ax^2+x+3

A quadratic expression
ax^2+bx+c is complete square if
b^2-4ac=0

For the given expression a=a,b=1 and c=3.


(1)^2-4(a)(3)=0


1-12a=0

Add 12a on both sides.


1=12a

Divide both sides by 12.


(1)/(12)=a

Therefore, the value of a is
(1)/(12).


(1)/(12)x^2+x+3


((1)/(2√(3))x)^2+2((1)/(2√(3))x)(√(3)+(√(3))^2


((1)/(2√(3))x+√(3))^2
[\because (a+b)^2=a^2+2ab+b^2]

User Arunkumar Ramasamy
by
8.1k points

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