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Solving the Equation (x-6)(x-6) = 0
This equation represents a simple quadratic equation in factored form. To solve for the value of x, we can utilize the following steps:
Understanding the Equation
The equation (x-6)(x-6) = 0 represents the product of two identical factors, (x-6) and (x-6), equaling zero.
The Zero Product Property
The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero.
Solving for x
Applying the Zero Product Property to our equation, we have:
- (x-6) = 0
Solving for x in this equation:
- x = 6
Since both factors are identical, the solution x = 6 is a double root for the equation.
Conclusion
The equation (x-6)(x-6) = 0 has one solution, x = 6, which is a double root. This means the solution x = 6 satisfies the equation twice.