Exploring Quadratic Functions and Inequalities
6. 3 Completing the Square
By: Sara G.
Barbie Kelly ran a red light and totaled her pink Barbie Convertible car. She went to the car dealership to pick up her fixed car, but the mechanic said that she could not get it until she solved a riddle. Barbie Kelly looked at the riddle and realized that solving it was just a matter of completing the square. Below is Barbie's steps in solving her riddle.
Her problem is x2 - 16x - 17 = 0 . Try the problem by yourself and then check your answers with Barbie Kelly's.
There are seven steps to completing the Square.
| Step 1: | Write the equation in standard form: ax2 + bx + c = 0. | x2 - 16x - 17 = 0 |
| Step 2: | Transfer the constant term. | x2 - 16x = 17 |
| Step 3: | Factor or divide the equation by the coefficient of x2. (There will not always be a coefficient in front of x2.) | x2 - 16x = 17 (There was no coefficient in front of the x2 so it stayed the same.) |
| Step 4: | Take 1/2 the coefficient of x, square it and add it to both sides of the equation. | x2 - 16 + 64 = 17 + 64 |
| Step 5: | Factor on the left and simplify on the right. | (x-8)2 = 81 |
| Step 6: | Take the square root of both sides of the equation. | the square root of (x-8)2 = x - 8 and the square root of 81 = 9 |
| Step 7: | Solve for x. |
x-8 = plus or minus 9 x = 17 x = -1 |
I would like to credit Wake County Algebra 2 Supplement for the seven written steps.
“Character is like a tree and reputation like its shadow. The shadow is what we think of it; the tree is the real thing.” — Abraham Lincoln, 19th-century U.S. president
This quote came from: http://www.josephsoninstitute.org/quotes/quotecharacter.htm
I chose this quote because I feel that character and reputation are sometimes mixed up. If a person has good character than they will have a good reputation because their character traits will show. A person's character is real. Their reputation is only what other people think of them.
I hope that I helped you understand completing the square. Here is another website you can visit if you would like some further help.
http://www.sosmath.com/algebra/quadraticeq/complsquare/complsquare.html