Question

9 times a certain whole number is equal to 5 less than twice the square of the number find the number

Answer 1

number = 5

Explanation:

let the whole number be n then 9 times the number is 9n and

twice the square of the number is 2n² , 5 less is 2n² - 5

equating the two expressions

2n² - 5 = 9n ( subtract 9n from both sides )

2n² - 9n - 5 = 0 ← quadratic equation in standard form

(n - 5)(2n + 1) = 0 ← in factored form

equate each factor to zero and solve for n

n - 5 = 0 ( add 5 to both sides )

n = 5

2n + 1 = 0 ( subtract 1 from both sides )

2n = - 1 ( divide both sides by 2 )

n = -
`(1)/(2)`

Since n is a whole number, then n = 5