mathamatics?

Question

completing the square...whats taht again? (gr.11)

Answer 1

Completing the square is a way to solve an equation when you cannot factor it. In order to complete the square you need an equation. We'll use x2+4x+2=0. You will need to move the number without a variable to the right side. Then we would have x2+4x=-2. Now, to complete the square, you take the number with the variable that doesn't have an exponent and divide it by 2 then square it. You add that number now to both sides. We'd now have x2+4x+4=2. That is how you complete the square. Of course, you'd need to finish the equation, but I trust you know how to do that since you just asked how to complete the square. Hope this helped. I am very sleepy right now, so I hope all this make sense :)

Answer 2

Most of the answers above are in the ballpark. When you complete the square, you're forming a perfect square trinomial and using it to solve an equation quadratic in something.

First off, the perfect squares. There are two of them:

(x + a)^2 = x^2 + 2ax + a^2

(x - a)^2 = x^2 - 2ax + a^2

Notice that the patterns are similar. In completing the square, you're going to start with something like the right-hand side of those equations and massage it into a perfect square, then factor it like the left-hand side.

Consider:

x^2 + 6x + 5 = 0

This is not a perfect square, but we can make it one. Look at the patterns above. Note that the coefficient of the linear term is always 2a, while the constant term is a^2. The coefficient we have here is 6, so 6 = 2a, telling us that a = 3. If this were to be a perfect square, then, it would have to be x^2 + 6x + 9. So - what do we have to do to this to get a perfect square? Obviously, we add 4:

x^2 + 6x + 5 = 0

x^2 + 6x + 5 + 4 = 0 + 4

x^2 + 6x + 9 = 4

And now we have a perfect square trinomial on the left - we have "completed the square". Now we can solve:

(x + 3)^2 = 4 Take the square root of both sides:

x + 3 = +/- 2

x = 3 +/- 2

x = 5 or x = 1

Answer 3

Ok. to complete the square:
say you have two variables, x and y, and say you have an equation like this:

x^2 + 2x + y^2 + 4y = 7

Now, to complete the squares, you want to be able to rewrite this as:

(x + a) ^2 + (y + b) ^2 = c

In order to do this, you divide the coefficients on x and y (2 and 4 respectively) by 2. so, you get 1 and 2. now you square these and you get 1 and 4. so, add 1 and 4 to both sides.

x^2 + 2x + 1 + y^2 + 4y + 4 = 7 + 4 + 1

Now you see, x^2 + 2x + 1 can be re-written as (x + 1) ^2
also, you see, y^2 + 4x + 4 can be rewritten as (y + 2) ^2

So, now you have:

(x + 1) ^ 2 + (y + 2) ^2 = 12

THAT's completing the square. and, i don't know if you know this, but this is now a nice equation for a circle. =) so you can solve for x and y very nicely.

Answer 4

I didn't really know (I never remember terminology) so I looked it up, I hope that helps

Completing the square is an algebra technique, used in algebra for (among other things) solving quadratic equations, in analytic geometry for discovering the shapes of graphs, and in calculus for computing integrals, including, but hardly limited to, the integrals that define Laplace transforms. The essential objective is to reduce a quadratic polynomial in a variable in an equation or expression to a squared polynomial of linear order. This can reduce an equation to one that one knows how to solve, or an integral to one that one knows how to evaluate.