Solving problems with Quadratic Equation

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Solving problems with Quadratic Equation:

Solving problems with Quadratic Equation

Hello this video will teach how to solve problems with quadratic equation :

Hello this video will teach how to solve problems with quadratic equation

A rectangular lot has an area of 96m2. What are the dimensions of the lot if it requires 40m of fencing materials to enclose it? :

A rectangular lot has an area of 96m 2. What are the dimensions of the lot if it requires 40m of fencing materials to enclose it?

First we should know what is the formula for a rectangular lot which is l * w = a and the formula for the perimeter of a rectangle which is 2l+2w=p :

First we should know what is the formula for a rectangular lot which is l * w = a and the formula for the perimeter of a rectangle which is 2l+2w=p Using these formulas, we can form a quadratic equation that can get the dimensions of the lot.

Next is we should substitute the given to these formulas and we would get: :

Next is we should substitute the given to these formulas and we would get: l * w= 96 2l + 2w= 40

Now we are going to focus first on the formula on how to get the area of a rectangle :

Now we are going to focus first on the formula on how to get the area of a rectangle

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Remove one of the two variables on the equations by multiplying both sides with either w or l and the result is : l= 96/w or w= 96/w depending on which variable are you removing. We will be using l=96/w but you can also use the other one because it will still give the same answer.

Next we will substitute what you result is to the formula on how to get the perimeter of a rectangle :

Next we will substitute what you result is to the formula on how to get the perimeter of a rectangle This is how it should look like: 2(96/w) + 2w) = 40

Next step is to make it into a quadratic equation It should be like this : 2w2-40w+192 :

Next step is to make it into a quadratic equation It should be like this : 2w 2 -40w+192

We will be solving for the roots by using quadratic formula but you can use any method you want. :

We will be solving for the roots by using quadratic formula but you can use any method you want.

First find a, b, and c Then let x be the width :

First find a, b, and c Then let x be the width

Then substitute these to the quadratic formula, it would look like these: :

Then substitute these to the quadratic formula, it would look like these:

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Continue solving it..

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Continue solving it..

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Then solve for X 1 and X 2 …..

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Then solve for X 1 and X 2 ……

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Then solve for X 1 and X 2 ……

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Then solve for X 1 and X 2 ……

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Then solve for X 1 and X 2 ……

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Then solve for X 1 and X 2 ……

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Then solve for X 1 and X 2 ……

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Then solve for X 1 and X 2 ……

X1=12 X2=8 :

X 1 =12 X 2 =8 Now we would just divide x1 and x2 to the area to get the length

The lengths are: :

The lengths are: l 1 =8 l 2 =12

Therefore the dimensions are 12x8 m :

Therefore the dimensions are 12x8 m

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