Complete trinomial perfect square x^2+10x then factor trinomial?
I am learning this new stuff and I don't get it please help!!!
- 8 years agoBest Answer
To complete the square you divide the linear term's coefficient (in this case, 10) by two, and then square it; which in this case that will be 25. So x^2 + 10x + 25 will be a perfect square trinomial.
To factor it, factor it like any other quadratic -- but note whenever you complete-the-square, the constant in the binomial square will always be half of the the linear term's coefficient: (x + 10/2)^2, or just (x + 5)^2.
To reinforce your understanding, it may be helpful to read up on the tutorial, or watch the video I listed below as source references.
If you need more help, please clarify where you are in the process and what's giving you trouble. I'd be more than happy to continue to assist.
- 8 years ago
Say you have a function 0 = ax^2 + bx + c, where a = 1, just like the binomial you suggested.
To complete the square, you must add 25. Why? But also add it to the other side!
If you take half of the second term (bx, where b = 10), then you've got 5x. To complete the square you square half of b, or (.5b)^2, so you know what you need to add to complete the square. Once you've added 25, you can then factor the trinomial 0 + 25 = x^2 + 10x + 25 into 25 = (x+5)^2, or 0 = (x+5)^2 - 25. -> y = (x+5)^2 - 25.
This can be completed where b is not an even number or an integer (b can also be a fraction!)
Let's try a case where a doesn't equal one, say, where a = 2, b = 10, and c = 9 -> 0 = 2x^2 + 10x + 9
Factor out the 2 from only the first two terms (important): 0 = 2(x^2 + 5x) + 9
Now, we take 1/2 of b, and then square it, so we know what to add or subtract to complete the square. But, we must add the same thing to both sides, so don't neglect the coefficient (the 2 we pulled out earlier). You can also subtract the same value on the same side of the equation so you don't have to do it later.
0 + 2(25/4) = 2(x^2 + 5x + 25/4) + 9 -> 25/2 = 2(x + 5/2)^2 + 9 -> 0 = 2(x + 5/2)^2 - 7/2 ->
y = 2(x+5/2)^2 - 7/2,
This is very simple and methodical, and I hope I helped you!Source(s): I am a high-school Calculus student!