Question

The difference of the square of a number and 9 is equal to 8 times that number. Find the positive solution.

Answer 1

`x {}^(2) - 9 = 8x \\ x {}^(2) - 8x - 9 = 0 \\ x = \frac{ - ( - 8) + \sqrt[]{( - 8) {}^(2) - 4(1)( - 9)} }{2( {1}^{}) }`

`x = (8 + √(64 + 36) )/(2) = (8 + √(100) )/(2) = (8 + 10)/(2) = 9`

Answer 2

Answer: x = 9

Explanation:

The difference of the square of a number and 9 is equal to 8 times that number. Find the positive solution.

let x = a number

`x^2-9=8x\\x^2-8x-9\\(x-9)(x+1)\\x-9 = 0\\x=9\\x+1=0\\x=-1`

taking only the positive solution, we get x = 9