# situations where quadratic equations are illustrated

2
by joyslligrace18

2014-06-19T11:34:24+08:00

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The square of number is decreased by 15. This value is twice the original number. Find the number(s). The answer is:

x-15=2x
x-2x-15=0
(x-5)(x+3)=0
x=5x  x=(-3)
You missed the ^2 :)
Thank you for correction!
2014-06-19T12:24:50+08:00

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The most common problems involving quadratic equations are finding the dimensions when the area is given.

Example:

Find the dimensions of a rectangular textbook whose length is 10cm longer than its width and covers an area of 375 cm².

Solution:

Let x be the width of the textbook
x+10 be the length of the textbook

A = width·length
375 = x (x+10)
375 = x² +10x
0 = x² +10x -375
0 = (x+25) (x-15)
x+25 = 0     ;     x-15 = 0
x = -25    ;     x = 15           (use x=15 because dimensions may never be negative)