Question

The square of the product of 4 and a number is the sum of the number and 15

Answer 1

The number is 1 or -0.94 ( to the nearest hundredth).

Explanation:

Let the number be x, then:

(4x)^2 = x + 15

16x^2 - x - 15 = 0

x = [-(-1) +/- sqrt(1 - 4 * 16 * -15)] / 32

x = 32/32 = 1 or

x = -0.94.

Answer 2

x=1 or x = -
`(15)/(16)`

Explanation:

To solve this problem, we will follow the steps below;

First, we need to re-write the question in a mathematical format.

Let x be the number

"The square of the product of 4 and a number is the sum of the number and 15" can be written mathematically as;

(4x)² = x + 15

16x² = x + 15

This equation can be re-written as;

16x² - x - 15 = 0

This is a quadratic equation, we can solve by formula method

x = -b ±√b² - 4ac /2a

From the equation above, a = 16 b = -1 and c= -15

We can now proceed to insert the values into the equation

x = -b ±√b² - 4ac /2a

x = -(-1) ±√(-1)² - 4(16)(-15) /2(16)

x = 1 ±√1 + 960 /32

x = 1 ±√961 /32

x = 1 ± 31 /32

Either x =
`(1+ 31)/(32)` or x =
`(1-31)/(32)`

x =
`(32)/(32)` or x =
`(-30)/(32)`

x=1 or x = -
`(15)/(16)`