Question

the square of number is smaller than 12 times the number by 32 .find the number.

Answer 1

Let the number be x. The square of a number, x² is smaller than 12 times the number by 32, i.e. 12x - x² = 32 => The equation above is quadratic, so....

If the number is x then 12 times the number is 12x.

The square of the number is x² so

12x - x² =32 giving

x²-12x+32=0 giving

(x-4)(x-8)=0 so x=4 or x=8

12x - 32 = x²

x² - 12x + 32 = 0

(x - 8)(x - 4) = 0

x = 8 , x = 4

Check

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12 x 8 - 8² = 96 - 64 = 32

12 x 4 - 4² = 48 - 16 = 32

Answer 2

Let the desired number be x

A/Q

${x}^{2} = \frac{12x}{32}$
$32 {x}^{2} = 12x \\ \frac{32 {x}^{2} }{x} = 12 \\ 32x = 12 \\ x = \frac{12}{32}$
$x = \frac{3}{8}$