Question

Complete each trinomial such that it can be rewritten in the form

a(x+b)^2 or a(x −b )^2


1.5x^2+6x+ ...

Answer 1

Let's see

• 1.5x²+6x=0

Find a as a perfect square

• √1.5=1.2

Find c by 2ab form

• 2ab=6
• 2(1.2)b=6
• 2.4b=6
• b=2.5

So

• b²=2.5²=6.25

Now

• (1.2x)²+2(1.22)(2.5)

Add and subtract b^2

• (1.2x)²+2(1.22)(2.5)+6.25-6.25
• (1.2x+2.5)²-6.25

Hang on! it's vertex form i.e a(x-h)²+k not our required form

To find the correct C we need

• A number which is multiple of a to satisfy ac rule

Round the b² we get while solving before

• 6.25≈6

Take 6?

• y=1.5x²+6x+6
• y=1.5(x²+4x+4)
• y=1.5(x²+2(2x)+2²)
• y=1.5(x+2)²

Satisfied

We have Done!

Answer 2

Explanation:

1.5x^2+6x+.... so that it can be rewritten in the form a(x+b)^2

Let .... be C

1.5x^2+6x+C

=1.5(x^2+4x+(C/1.5))

Compare above with 1.5(x+2)^2 = 1.5(x^2+4x+4)

C/1.5=4

C=6

So the expression should be 1.5x^2+6x+6

It can be rewritten to 1.5(x+2)^2