Word problems on Quadratic Equations (2)

Question:

Think of a number, square it and subtract the same number from it, the result is 72. What is the number?

Solution:

Let the number = x
Therefore square of the number = x^2
Subtracting the squared number with original number = 72

x^2 - x = 72
x^2 - x + 72 = 0
x^2 - 9x - 8x + 72 = 0
x(x - 9) -8(x - 9) = 0
(x - 9) (x - 8) = 0
(x - 9) = 0   (x - 8) = 0
x = {9, 8}

In word problems it is often necessary to verify each solution again because some solutions can be extraneous solutions,
For x = 9,

x^2 - x= 9^2 - 9 = 81 - 9 = 72

For x = 8,

x^2 - x = 8^2 - 8 = 64 - 8 = 56

Answer:

Since x =  8 does not fit the conditions given in the word problem, hence the answer is x = 9

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Word Problem 3 (Quadratic Equations)