Q: Let's say you're working with the following equation: 3x2 - 4x + 5. To factor out a three from the first two terms, simply pull out a 3 and place it around a set of parenthesis around both terms, while dividing each term by 3. 3x2 divided by 3 is simply x2 and 4x divided by 3 is 4/3x. So, the new equation should look like this: 3(x2 - 4/3x) + 5. The 5 will remain outside of the equation because you did not divide it by 3. The second term, also known as the b term in the equation, is 4/3. Halve the second term, or divide it by 2 first. 4/3 2, or 4/3 x 1/2, is equal to 2/3. Now, square this term by squaring both the numerator and denominator of the fraction. (2/3)2 = 4/9. Write this term down. You'll need this "extra" term to turn the first three terms in this equation into a perfect square. But you have to remember that you added it by subtracting it from the equation as well. Though obviously, it won't do you much good to simply combine the terms -- you'll be back where you started. The new equation should look like this: 3( x2 - 4/3 x + 4/9 - 4/9) + 5. Since you're working with a coefficient of 3 outside the parentheses, you can't just pull out the -4/9. You'll have to multiply it by 3 first. -4/9 x 3 = -12/9, or -4/3. If you're not working with an equation with a coefficient other than 1 over the x2 term, then you could skip this step. Right now, you're left with 3(x2 -4/3x +4/9) within the parentheses. You worked backwards to get the 4/9, which was really another way of finding the term that would complete the square. So, you can rewrite those terms like this: 3(x - 2/3)2. All you had to do was halve the second term and remove the third. You can check that this works by multiplying it out to see that it gives you the first three terms of the equation. 3(x - 2/3)2 = 3(x - 2/3)(x -2/3) = 3[(x2 -2/3x -2/3x + 4/9)] 3(x2 - 4/3x + 4/9) You're left with two constant terms, or terms that aren't attached to a variable. Right now, you're left with 3(x - 2/3)2 - 4/3 + 5. All you have to do is add up -4/3 and 5 to get 11/3. You do this by setting them to the same denominator: -4/3 and 15/3, and then adding the numerators to get 11, and keeping the denominator as 3. -4/3 + 15/3 = 11/3. You're all done. The final equation is 3(x - 2/3)2 + 11/3. You can remove the coefficient of 3 by dividing both parts of the equation to get (x - 2/3)2 + 11/9. You have now successfully placed the equation into vertex form, which is a( x - h )2 + k, where k represents the constant term.
A: Write down the equation. Factor out the coefficient of the squared term from the first 2 terms. Halve the second term and square it. Add and subtract this term from the equation. Pull the term you subtracted out of the parenthesis. Convert the terms in the parentheses into a perfect square. Combine the constant terms. Write the equation in vertex form.

Q: It may sound gross, but having day-old hair actually helps the tiara stay on better. If you must wash your hair, avoid using conditioner. This will give your hair some texture and "grip," and help the tiara stay on longer. This include applying hairspray. If you apply hairspray after you put on your tiara, you will dull the surface and make it sticky. Try to angle it slightly, so that the prongs go into your hair. It will blend in better with your hairstyle. Try not to just plop it on top of your head. To ensure that the tiara will not fall off, use bobby pins to hold it in place. Place the bobby pins in such a manner that they will be hidden, and will not interfere with the design of the tiara. This will cause the tiara to drag back painfully. Instead, put the tiara on first, then clip the veil directly to your hair.
A: Don't wash your hair. Style your hair first. Slide the tiara carefully in the middle of the head. Use bobby pins to secure the tiara. Don't clip veils to tiaras.

Q: Adding other items from your wardrobe can really personalize your costume and make it your own. Add a contrasting belt to give your gown more shape, light colored leggings for even more color, or gloves to really bring it home. Add your own rings, earrings, bracelets and necklaces to really achieve an elegant angel look. If you're leery about going out in your finest accessories, consider visiting a costume or party supply store for costume jewelry. You can also add splashes of glitter, light-colored paint or even tin foil to really make the outfit pop. Make sure your footwear matches the rest of your outfit. If you've gone the traditional angel route, keep the footwear limited to sandals. If you're going for a more elegant angel look, make sure your footwear is formal, such as simple slip-on white shoes. The last thing you want to do is have your well-crafted costume thrown off by a pair of sneakers.
A:
Add other wardrobe items. Accessorize. Keep your footwear angelic.