SOLUTION: Hello, I am preparing for a test and I would like to know how to solve problems using a quadratic equation. For example : "The length of a book is 4 cm more than its width and the

Question 1044324: Hello, I am preparing for a test and I would like to know how to solve problems using a quadratic equation. For example : "The length of a book is 4 cm more than its width and the area of the face of the book is 320 cm^2. Find the dimensions of the face of the book."
Found 3 solutions by josgarithmetic, Theo, ikleyn:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
y is for length
x is for width
-

This will give you one quadratic equation. This example allows for simple substitution to create or form the quadratic equation.

-------you would have learned how to solve this kind of equation already. Can the trinomial be factored? Yes, it seems factorable.

...

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the first thing you have to do is to translate the problem into an algebraic equation.

if it is linear, you then solve the linear equation.

if it is quadratic, you then solve the quadratic equation.

a quadratic equation is an equation in which the highest exponent of any term is equal to 2.

your problem states:

The length of a book is 4 cm more than its width and the area of the face of the book is 320 cm^2.

you should know that length * width = area.

you are given that the length of the book is 4 cm more than its width.

you need to translate this to an algebraic expression.

let x equal the length.

since the with is equal to 4 cm more than the length, you get:

length = x

width = x + 4.

since length * width = area, you get:

x * (x + 4) =area

since area = 320 cm^2, you get:

x * (x + 4) = 320

you don't always show the unis involved (like cm and cm^2), but they're implied and they have to be consistent with each other.

now that you have your equation, you need to simplify it so you can solve it.

simplify by applying the distributive law to get:

x^2 + 4x = 320

subtract 320 from both side of the equation to get:

x^2 + 4x - 320 = 0

the equation is now in standard form of a quadratic equation and can be factored using one of various method.

factor the equation to get (x + 20) * (x - 16) = 0

solve for x to get:

x = -20 or x = 16.

x can't be negative, so x = 16 is your answer.

the length is equal to x which is equal to 16 centimeters..

the width is equal to x + 4 which is equal to 20 centimeters.

length times width = 16 * 20 = 320 square centimeters.

there are various methods to factor a quadratic equation.

here are some lessons that show you how to do them.

http://www.purplemath.com/modules/factquad.htm

http://www.purplemath.com/modules/factquad3.htm

http://www.purplemath.com/modules/quadform.htm

http://www.regentsprep.org/regents/math/algtrig/atv1/revfactorgrouping.htm

there are even more methods, such as the indian method, that are not commonly used.

i used the factor by grouping method most of the time.

if you get stuck and can't factor the quadratic by any other means, then use the quadratic formula.

but first you need to get it into standard form.

the standard form of a quadratic equation is ax^2 + bx + c = 0

a is equal to the coefficient of the x^2 term.
b is equal to the coefficient of the x term.
c is equal to the constant term.

Answer by ikleyn(52775)   (Show Source): You can put this solution on YOUR website!
.
You will find solved problems similar to this in the lessons
    - Problems on the area and the dimensions of a rectangle
    - Problems on the area and the dimensions of a rectangle surrounded by a strip
    - Problems on a circular pool and a walkway around it
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

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