How to Solve a Quadratic Equation by Completing the Square ?
Make sure the leading coefficient is 1. This is the number in front of the X squared. If it isn’t 1, divide everything in the problem by the leading coefficient.
For instance,if you have 3 X squared, divide everything by 3. If you get fractions, don’t panic! You will just have to take your time to work with fractions through the problem.
Move the constant (the plain number with no X in it) over to the right side by adding or subtracting it from both sides. Do the opposite of whatever is in the original equation.
Find “b.” This is the number in front of the plain X, not the X squared. Write “b” down off to the side.
Make sure you include a negative sign if there is one in front of the “b”. Then divide it by two and circle Than square that and put a box around your answer.
Add the number in the box to both sides of the equation.
Now you are going to completely rewrite the left side of the equation. You are basically saying what could I foil (multiply out) that would make what I have now? Luckily, completing the square tells you how to do this so you don’t have to figure it out.
Draw parenthesis. Inside the parenthesis write “X + your circled number” if the number is positive or “X – your circled number” if it is negative Then put a “squared” on the outside of the parenthesis.
Now you can take the square root of both sides to solve for X. Because you are putting a square root sign in, you need to have two equations. One with a positive answer and one with a negative.
If you are able to take a square root of the right side, you will end up with two integer answers as in this problem.
If you cannot take the square root you need to simplify the radical in both equations and finish solving for X by adding/subtracting the remaining number on the left to both sides.
Many real world situations that model quadratic functions are data driven What happens when you are not given the equation of a quadratic function, but instead you need to find one?
In order to obtain the equation of a quadratic function, some information must be given Significant data points, when plotted,may suggest a quadratic relationship, but must be manipulated algebraically to obtain an equation.
Remembering: It is read minus b plus or minus the square root of b-squared minus four ac, all over two a It’s like driving a car once you know it, you won’t forget it: it takes you places fast.
Application – The “±” means you need to do a plus AND a minus, and therefore there are normally TWO solutions! You don’t have to choose, I’ll take both.
the sources:
http://zonalandeducation.com







