Question

when 3 times a number is added to the square of a given number,the result is 54.what is the number

Answer 1

Let's the number be x

3x+x²=54
x²+3x-54=0
x²+9x-6x-54=0
x(x+9)-6(x+9)=0
(x-6)(x+9)=0
So, the number can be either 6 or -9

Answer 2

The required number can be 6 or -9.

Given:

Three times a number added to the square of number = 54

To find:

The required number

Solution:

Let the required number be x.

According to the question,

Three times of x + square of x = 54

Putting the information in a mathematical equation,

3x + x² = 54

Transposing all terms to LHS, we get

⇒ x² + 3x - 54 = 0

Solving the equation through the factorisation method:

x² + 3x - 54 = 0

⇒ x² + 9x - 6x - 54 = 0

⇒ x(x + 9) - 6(x + 9) = 0

⇒ (x - 6)(x + 9) = 0

⇒ x = 6 or x = -9

∴ The required number can be 6 or -9.

SPJ2