If you are citizen of an European Union member nation, you may not use this service unless you are at least 16 years old.
You already know Dokkio is an AI-powered assistant to organize & manage your digital files & messages. Very soon, Dokkio will support Outlook as well as One Drive. Check it out today!

Solving-Quadratics

Page history last edited by Kristen Fouss 15 years, 3 months ago

QUADRATIC EQUATION: any equation in the form $eq=ax^2+bx+c=0$ where (a) does not equal zero.

Any value that satisfies this equation is called a root, zero, or solution of the equation.

THERE ARE THREE WAYS TO SOLVE A QUADRATIC FORMULA:

1) Factoring

2) Completing the square

3) Quadratic Formula

1) FACTORING

the resolution of an entity into factors such that when multiplied together they give the original entity

the act or process of separating an equation, formula, cryptogram

$eq=x^2+2x-8=0$

(x-2)(x+4)=0

x=2,-4

Find two number that when multiplied together equal C, but also add together to get B. If a does not equal 1, then you must first factor it out of each term. So, 4 and -2 multiply to be -8 and add together to positive two. Then use each term and set them equal to zero. Solve for x and those will be your solutions to the quadratic equation through factoring.

Please Note: Factoring will not always work and one of the other methods will be needed to solve the problem.

Here are some fun problems that you will expand your mind on the method of factoring: http://library.thinkquest.org/29292/quadratic/2factoring/practice.htm

2) COMPLETING THE SQUARE

will also help solve quadratic equations and is just another method if factoring is not possible and you can not remember the quadratic formula. First make sure that A=1. If this is not true, factor A out of each term.

$eq=x^2+6x+11=0$ (Since no two numbers can be multiplies by 11 and add to six we must use this method)

FIRST MOVE C TERM TO THE OTHER SIDE.

$eq=x^2+6x=11$

THEN TAKE (B/2) AND SQUARE THAT NUMBER.

(6/2)=3 3^2=9

NEXT, ADD THAT NUMBER TO BOTH SIDES.

$eq=x^2+6x+9=20$

FACTOR THE LEFT AND SET IT EQUIL TO THE RIGHT.

$eq=(x+3)^2=20$

SQUARE EACH SIDE TO GET RIDE OF THE SQUARE ON THE LEFT.

$eq=x+3=\pm\sqrt{20}$

SOLVE FOR X.

$eq=x=-3\pm\sqrt{20}$

This method will work for any quadratic equation, but sometimes the solutions could be pretty messey so then you would want to move on the quadratic formula. Which will be our next stop on the journey through the wonderful world of quadratics.

Click this link to try some completing the square exercises. http://www.mathisfunforum.com/viewtopic.php?pid=38653

3) QUADRATIC FORMULA

THIS METHOD WORKS FOR ANY QUADRATIC EQUATION, EVEN WHEN IT CAN NOT BE FACTORED OR COMPLETING THE SQUARE IS JUST WAY TO DIFFICULT.

The formula is as follows: $eq=x=(-b\pm\sqrt(b^2-4ac))/2a$

Once you have plugged in all of the numbers, use your outstanding math skills to find the zeros or solutions to the equation. Notice the plus or minus in the equation, signifying there will be two outcomes.

Here is a wonderful video on solving quadratics http://video.google.com/videoplay?docid=6750617731762388525&ei=P6tGSaWjIIWiqgK0zcHtDA&q=quadratic+equations&hl=en