Suppose that four times the square of a number equals 20 times that number. Whatis the number?

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4 n^2 = 20n

zero is one solution. Solve for n.

Worst

To find the value of n, we can solve the given equation step by step.

Step 1: Rewrite the equation:
4n^2 = 20n

Step 2: Simplify the equation:
4n^2 - 20n = 0

Step 3: Factor out the common variable n:
n(4n - 20) = 0

Step 4: Set each factor equal to zero and solve for n:
n = 0 or 4n - 20 = 0

For the first case, n=0.

Step 5: Solve the second equation for n:
4n - 20 = 0
4n = 20
n = 20/4
n = 5

Therefore, the solutions to the equation 4n^2 = 20n are n = 0 and n = 5.

To find the number that satisfies the equation "four times the square of a number equals 20 times that number," we can follow these steps:

1. Start with the equation: 4n^2 = 20n
Here, "n" represents the unknown number we are trying to find.

2. Simplify the equation by dividing both sides by 4:
(4n^2) / 4 = (20n) /4
This simplifies to: n^2 = 5n

3. Rearrange the equation to one side and set it equal to zero:
n^2 - 5n = 0

4. Factor out the common factor of "n" from the left side of the equation:
n(n - 5) = 0

5. Apply the zero-product property, which states that if the product of two factors is zero, then at least one of the factors must be zero:
Therefore, either n = 0 or (n - 5) = 0

6. Solve each equation separately:
a) n = 0
This means that the number is 0.

b) (n - 5) = 0
Add 5 to both sides:
n = 5
This means that the number is 5.

So, the possible values for the number that satisfies the equation are 0 and 5.