7x³ = 28x is our equation. We want its solutions.
When you have x and different powers, set the whole thing equal to zero.
7x³ = 28x
7x³ - 28x = 0
Now notice there's a common x in both terms. Let's factor it out.
x (7x² - 28) = 0
As 7 is a factor of 7 and 28, it too can be factored out.
x (7) (x² - 4) = 0
We can further factor x² - 4. We want a pair of numbers that multiply to 4 and whose sum is zero. The pairs are 1 and 4, 2 and 2. If we add 2 and -2 we get zero.
x (7) (x - 2) (x + 2) = 0
Now we use the Zero Product Property - if some product multiplies to zero, so do its pieces.
x = 0 -----> so x = 0
7 = 0 -----> no solution
x - 2 = 0 ----> so x = 2 after adding 2 to both sides
x + 2 = 0 ---> so = x - 2 after subtracting 2 to both sides
Thus the solutions are x = 0, x = 2, x = -2.
Answer:
<h2>6</h2>
Step-by-step explanation:
Answer:
About 0.41 hours
Step-by-step explanation:
THe distance between Michael and Clara is 44 km.
We know D = RT,
Where
D is distance
R is rate (speed)
T is time
For Michael, we can write:
D = 47t
For Clara, we can write:
D = 61t
If we let michael's distance be x, Clara's distance would be 44 - x
So, we can say:
x = 47t
and
44 - x = 61t
Putting first equation into 2nd, we get:
44 - 47t = 61t
SOlving:
44 - 47t = 61t
44 = 61t + 47t
44 = 108t
t = 44/108 = 0.41 hours
The commute took 0.41 hours
