If 2 times the square of a number is equal to the 6 times the number,find the number
2x^2 = 6x
2x^2 - 6x = 0
2x(x - 3) = 0
x = 0 or x = 3
check:
if x = 3
2(3)^2 = 18
6(3) = 18 , YUP!
if x = 0
2(0) = 0
6(0) = 0 , YUP!
Well, let's make the equation a little less serious and have some fun with it!
If 2 times the square of a number is equal to 6 times the number, we can express that as:
2x^2 = 6x
Now, let's divide both sides by 2 to simplify things:
x^2 = 3x
Alright, now let's bring all the terms to one side to form a quadratic equation:
x^2 - 3x = 0
Now, if we factor out an "x", we get:
x(x - 3) = 0
To find the values of "x" that satisfy this equation, we set each factor equal to zero:
x = 0 or x - 3 = 0
So, we have two possible solutions: x = 0 or x = 3.
Therefore, the number we're looking for could be either 0 or 3. It seems like the joke's on us this time, as there are two possible answers!
To find the number, follow these steps:
Step 1: Let's represent the unknown number as 'x'.
Step 2: According to the given information, 2 times the square of the number is equal to 6 times the number. This can be written as:
2x^2 = 6x
Step 3: Simplify the equation by subtracting 6x from both sides:
2x^2 - 6x = 0
Step 4: Factor out the greatest common factor, which is 2x:
2x(x - 3) = 0
Step 5: Set each factor equal to zero and solve for 'x':
2x = 0 or x - 3 = 0
Solving the first equation, we find that x = 0.
Solving the second equation, we find that x = 3.
Therefore, the number can either be 0 or 3.
To find the number, we can solve the given equation step by step.
Let's start by translating the given sentence into an equation.
"2 times the square of a number is equal to 6 times the number"
Let's assume the number is "x".
According to the sentence, we have:
2(x^2) = 6x
To solve this equation, we'll first simplify it by dividing both sides by 2:
(x^2) = 3x
Now, we have a quadratic equation. To solve it further, we'll move all the terms to one side:
(x^2) - 3x = 0
Next, we'll factorize the equation (if possible) by finding common factors:
x(x - 3) = 0
Now, using the zero-product property, we can set each factor equal to zero and solve for x:
1) x = 0
2) x - 3 = 0
For the first equation, x equals zero. However, zero does not satisfy the original equation since 2(0^2) does not equal 6(0).
For the second equation, by solving for x, we find:
x = 3
Therefore, the number we are looking for is 3.