X⁴=625x²
To solve for x, we can simplify the equation by factoring it.
X⁴ - 625x² = 0
We notice that both terms have a common factor of x²:
x²(x² - 625) = 0
Now we can solve for x²:
x² = 0 or x² = 625
If x² = 0, then x = 0.
If x² = 625, then x = ±25.
Therefore, the solutions for the equation X⁴ = 625x² are x = 0 or x = ±25.
To solve the equation X⁴=625x², we can start by rearranging the equation to one side and setting it equal to zero:
X⁴ - 625x² = 0
Next, we notice that both terms have a common factor of x². We can factor out x² from both terms:
x²(X² - 625) = 0
Now, we can apply the difference of squares formula to factor the expression in the parentheses:
x²((X + 25)(X - 25)) = 0
So, we have two factors: x² = 0 and (X + 25)(X - 25) = 0.
For the first factor, x² = 0, we can take the square root of both sides to solve for x:
x = 0
For the second factor, (X + 25)(X - 25) = 0, we set each factor equal to zero and solve for X:
X + 25 = 0 or X - 25 = 0
Solving these equations, we get:
X = -25 or X = 25
Therefore, the solutions to the equation X⁴ = 625x² are:
X = -25, X = 25, and x = 0.
To solve the equation X⁴ = 625x², we can start by rearranging the equation and factoring out a common term.
Step 1: Rewrite the equation
X⁴ - 625x² = 0
Step 2: Factor out a common term
We can notice that both terms have a factor of x². So, we can rewrite the equation as:
x²(X² - 625) = 0
Step 3: Factor the quadratic term
Now, we have a quadratic term, X² - 625, which can be factored further.
(x - 25)(x + 25) = 0
Step 4: Solve for x
Setting each factor to zero, we can solve for x:
x - 25 = 0 or x + 25 = 0
Solving each equation:
x = 25 or x = -25
Therefore, the solutions to the equation X⁴ = 625x² are x = 25 and x = -25.