### 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 = xTherefore square of the number = x^2

Subtracting the squared number with original number = 72

x^2 - x = 72In word problems it is often necessary to verify each solution again because some solutions can be extraneous solutions,

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}

For x = 9,

x^2 - x= 9^2 - 9 = 81 - 9 = 72For x = 8,

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

The quadratic formula is used to solve a very specific type of equation, called a quadratic equation. These equations are usually written in the following form:

ReplyDeleteax2 + bx + c = 0