## MAT 120 College Algebra: Quadratic Equations in One Variable

Presented by UMO SI leader Hannah Brown, this video explains how to Solve Quadratic Equations in one variable.

mat120-1.7a.pptx |

## Video Script:

This is for the Academic Resource Center for the University of Mount Olive

We are going to be discussing Quadratic Equations in One Variable

Say the variable x, is an equation that can be transformed into the form

ax^2+bx+c=0, where a,b, and c are real numbers and a≠(is not equal to)0. Such equations are also called second degree equations, as x is raised to the second power

We are going to start with a function

37y+11y^2=28

The first thing that you need to do is to rewrite the equation so that 0 appears by itself on one side.

11y^2+37y-28=0

The second thing that you need to do is to find two integers whose product is ac and whose sum is b. (If this is not possible, then the trinomial is not factorable.)

ac=11×-28=-308

We are trying to find two factors that when you multiply them together (44 times -7) equals – 308

-308=44 ×-7

When you add the two factors together (44 added with -7) it has to equal 37 which is b, the middle term

44-7=37=b

Our next part is going to be splitting these two terms up. We are going to rewrite the middle term (bx) using the two numbers found in step 2 as coefficients as shown.

(11y^2+44y)(-7y-28)=0

The next part is to break them up by factoring by grouping the first two terms and the last two terms. So from 11y^2 you are taking out 11y leaving y in the parentheses. When you are taking out 11y from the 44y, you are left with just 4 in the parentheses.

In the second part, when -7 is pulled out you are left with y+4.

11y(y+4)-7(y+4)=0

Having y+4 on both sides indicates that you have done the problem right. Factor out the common binomial factor

(11y-7)(y+4)=0

Then, you solve for y, you need to know what terms y can equal. First you have

(11y-7)=0 and (y+4)=0

When you add 7 on both sides, you are left with 11y=7, then you divide 11 on both sides leaving you with y=7/11

When you minus 4 from both sides, you are left with y=-4

Pause this video and try this problem on your own as follows

2x^2+9x+10

After doing this on your own your answer to this problem should be

b x=-2 and x=-5/2

We are going to be discussing Quadratic Equations in One Variable

Say the variable x, is an equation that can be transformed into the form

ax^2+bx+c=0, where a,b, and c are real numbers and a≠(is not equal to)0. Such equations are also called second degree equations, as x is raised to the second power

We are going to start with a function

37y+11y^2=28

The first thing that you need to do is to rewrite the equation so that 0 appears by itself on one side.

11y^2+37y-28=0

The second thing that you need to do is to find two integers whose product is ac and whose sum is b. (If this is not possible, then the trinomial is not factorable.)

ac=11×-28=-308

We are trying to find two factors that when you multiply them together (44 times -7) equals – 308

-308=44 ×-7

When you add the two factors together (44 added with -7) it has to equal 37 which is b, the middle term

44-7=37=b

Our next part is going to be splitting these two terms up. We are going to rewrite the middle term (bx) using the two numbers found in step 2 as coefficients as shown.

(11y^2+44y)(-7y-28)=0

The next part is to break them up by factoring by grouping the first two terms and the last two terms. So from 11y^2 you are taking out 11y leaving y in the parentheses. When you are taking out 11y from the 44y, you are left with just 4 in the parentheses.

In the second part, when -7 is pulled out you are left with y+4.

11y(y+4)-7(y+4)=0

Having y+4 on both sides indicates that you have done the problem right. Factor out the common binomial factor

(11y-7)(y+4)=0

Then, you solve for y, you need to know what terms y can equal. First you have

(11y-7)=0 and (y+4)=0

When you add 7 on both sides, you are left with 11y=7, then you divide 11 on both sides leaving you with y=7/11

When you minus 4 from both sides, you are left with y=-4

Pause this video and try this problem on your own as follows

2x^2+9x+10

After doing this on your own your answer to this problem should be

b x=-2 and x=-5/2