Solve by using the Quadratic Formula
PART 3:
Solve quadratic equations by using the QUADRATIC FORMULA
Factoring Quadratic trinomials is very important . What are they?
Example of a very simple Quadratic: They have 3 terms one of which has x^{2} , another
x, and the third term has no variable at all. There is a number in each of the three terms.
ax^{2} + bx + c where a ,b ,and c represent numbers is the general form of a quadratic trinomial.
The a and b and c are the numbers. The "a" can not be zero, but the b and c could be.
In this lesson we will study only quadratic trinomials
where none of the numbers are zero.
Here are some examples of quadratic trinomials with one variable (x).
We use the letter "a" to name the number coefficient of x^{2} , and we use "b" for x, and we use "c" for the number that stands by itself.
3x ^{2} + 6x - 4, thus
a = 3
b = 6
c = - 4
x ^{2} +15, thus
a = 1
b = 0
c =15
- 2x ^{2} - 6x - 4, thus
a = - 2
b = - 6
c= - 4
2x ^{2} - 6x , thus
a= 2
b=-6
c= 0
There are several methods used to teach factoring quadratics.
This lesson teaches the quadratic formula method. We can use it for all quadratic equations.
Can you solve 7x^{2} - 11x =6 ?
First you MUST move the 6 to the left side. We must write the equation in the correct form FIRST.
Then find a, b, and c as I did above.
If you do not know these or if you mix them up your answer will be wrong. Be sure you know a, b, and c.
7x^{2} - 11x -6 =0
Thus a=7 b= -11 and c= -6. Be sure you have the signs right.
HERE IS A VIDEO TO WATCH. You should watch it more than once.
Try a few problems and then watch it again.
You will better understand all the steps and remember them too if you will watch it more than once and after you have tried a few.
Watch the signs! You may need to click the x on the ad or click "SKIP AD" when the video starts.
VIDEO
Here is the link to it a youtube if you do not see it above: https://www.youtube.com/watch?v=3ayhvAI3IeY
Now see if you can solve : 7x^{2} - 11x -6 =0.
Then watch the video again.
7x^{2} - 11x -6 =0
x= +11 +or- sqrt[ 121 - 4(7)(-6)] All divided by 2(7).
x= 11+or - sqrt[ 121+168] all over 14. I mean that the 14 is under the LONG fraction bar.
x= 11+ sqrt[289] allover 14 and x= 11- sqrt[289] all over 14
Do you know square root of 289? It is 17.
So we have two answers to simplify.
x=11+17 all over 14 which is 28/14 = 2
and we have 11-17 all over 14 which is -6/14 = -3/7.
Sometimes the number under the square root is not a perfect square as the 289 was above.
In the video above be sure you understand what he did in his last steps. His number was 44 which is not a perfect square
Many problems will need to be completed with all the steps that he showed you.