Question

when 4 times a number is added to the square of the same number the result is 96 what is the number​

Answer 1

$\bf \underline{Answer:}$

8

$\bf Step-by-step \: explanation:$

Let the required number be x. Then, four times the number is 4x.

$\sf \underline{According \: to \: the \: question ;}$

x² + 4x = 96

⇒ x² + 4x - 96 = 0

⇒ x² + 12x - 8x - 96 = 0

⇒ x ( x + 12 ) - 8 ( x + 12 ) = 0

⇒ ( x + 12 ) ( x - 8 ) = 0

So, the possible value of x can be :

⇒ x + 12 = 0

⇒ x = - 12 [ rejected ]

And,

⇒ x - 8 = 0

⇒ x = 8

$\bf Hence, \: the \: required \: number \: is \: 8.$

Answer 2

Hola ❣️

Let the required number be x. Then, four times the number is 4x.

According to the question ;

x² + 4x = 96

=> x² + 4x - 96 = 0

=> x² + 12x - 8x - 96 = 0

=> x ( x + 12 ) - 8 ( x + 12 ) = 0

=> ( x + 12 ) ( x - 8 ) = 0

So, the number is

=> x + 12 = 0

=> x = - 12 [ rejected ]

Also,

=> x - 8 = 0

=> x = 8

Hence, the required number is 8.

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