2 radical x = x
What is the value of x?
Please explain
In this step, we are trying to factor the equation x^2 - 4x = 0, so we can easily find the values of x that make the equation true.
We can factor x out of the equation to get:
x(x - 4) = 0
Now we have two factors: x and (x - 4). These two factors multiply together to give us the original equation.
From the zero product property, we know that if the product of two factors equals zero, then at least one of the factors must be zero.
In this case, that means either x = 0 or (x - 4) = 0, which gives us x = 4. These are the two solutions to the equation.
So x^2 - 4x = 0, which we can factor to get x(x - 4) = 0, and we can solve for x by setting each factor equal to zero.
The given equation is 2√x = x.
First, we can square both sides to eliminate the radical:
(2√x)^2 = x^2
4x = x^2
Now we can simplify by subtracting 4x from both sides:
0 = x^2 - 4x
Factoring out an x:
0 = x(x - 4)
Therefore, the value of x can either be 0 or 4, since either x = 0 or x - 4 = 0. However, we need to check if either of these solutions work in the original equation:
If x = 0, then 2√0 = 0, which is true.
If x = 4, then 2√4 = 4, which is also true.
Therefore, the solutions are x = 0 or x = 4.
I am having trouble understanding how x^2 - 4x = 0
Thank you!
You're welcome! Feel free to ask if you have any other questions.
To find the value of x, we can start by isolating the radical term on one side of the equation.
Given:
2 radical x = x
To isolate the radical, we can start by squaring both sides of the equation:
(2 radical x)^2 = x^2
Expanding the left side of the equation:
4(x) = x^2
This equation tells us that 4 times x is equal to x squared.
Now, let's rearrange the equation to have all terms on one side:
0 = x^2 - 4x
Next, we can factor the quadratic equation:
0 = x(x - 4)
To find the values of x that satisfy the equation, we set each factor equal to zero:
x = 0 or (x - 4) = 0
For x = 0, the equation is satisfied. For x - 4 = 0, we can solve for x:
x - 4 = 0
x = 4
Therefore, the value of x is either 0 or 4.
To find the value of x in the equation 2√x = x, we can start by squaring both sides of the equation. This will help eliminate the radical sign (√).
Let's square both sides of the equation:
(2√x)^2 = (x)^2
Squaring the left side:
4x = x^2
Rearranging the equation:
x^2 - 4x = 0
Now, let's factor out x from the equation:
x(x - 4) = 0
To find the value of x, we can set each factor to 0 and solve for x:
x = 0
x - 4 = 0
x = 4
Therefore, the equation 2√x = x has two possible solutions for x: x = 0 and x = 4.