iUsername
Answered

Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

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+ ...

Sagot :

Answer:

Step-by-step 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

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!

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.