Completing the Square

Completing the Square
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  • I don't understand, what is completing the square and how do i do it? What are the steps again?
  • ?
  • -3x2+30x-1
  • ?
  • ?
  • uhhhh ok.....?
  • Sounds like someone needs some help! I'm mr. Square and helping you will make my life complete.
  • -3x2+30x-1
  • -3(x2-10x+25)+74
  • -3(x2-10x)-1
  • The first step is to factor the x2 coefficient out of the first two terms only (leave the third constant term)
  • i see....*yawn*
  • Next, look at the second term within the new brackets you've created. look at is's coefficiant, devide it by two and square it to get a new number.
  • -3(x2-10x)-1
  • -3(x2-10x+25-25)-1
  • (-10÷2)2=25
  • Now add this new number into the brackets beside the x term, and subtract it right after (but dont simplify the two to zero!)
  • Our next step is to multiply out the subtracted version of the number we just added to the inside of the rackets so its outside the brackets with the other constant term, which you can combine it with
  • =-3(x2-10x+25)+74
  • -3(x2-10x+25)-1+75
  • -3(x2-10x+25-25)-1
  • Now we have created a perfect-square trinomial expression inside the brackets, we are almost done.
  • (-3) X (-25)=75
  • -3(x-5)2+74
  • √
  • √25 =5 √x2 = x - means we subtract
  • Wow, i think i know how to do it now! Thanks for being so straight with me, maybe you arent a square after all!
  • -3x2+30x-1 = -3(x-5)2+74
  • And now were done! The square is completed and the equation is now in vertex form with the coordinates of the vertex and transformations clearly visible. 
  • THE END
  • Oh, so the square we are completing is the trinomial....
  • To represent our perfect square trinomial as the square of a binomial expression, we must take the square root of the first and third terms of the trinomial and add or subtract the two in a new set of brackets, depending on the sign of the coefficiant of the second term of our trinomial. Now write this new expression in a new set of brackets in the place of the old one, and put it to the power of 2.
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