Respuesta :
Answer:
The number is 1 or -0.94 ( to the nearest hundredth).
Step-by-step 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:
x=1 or x = - [tex]\frac{15}{16}[/tex]
Step-by-step 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 = [tex]\frac{1+ 31}{32}[/tex] or x = [tex]\frac{1-31}{32}[/tex]
x = [tex]\frac{32}{32}[/tex] or x =[tex]\frac{-30}{32}[/tex]
x=1 or x = - [tex]\frac{15}{16}[/tex]
