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(x-4)(x-4)=0

2 min read Jun 17, 2024
(x-4)(x-4)=0

Solving the Equation (x - 4)(x - 4) = 0

This equation represents a quadratic equation in factored form. To solve for the value of 'x' that satisfies the equation, we can utilize the Zero Product Property. This property states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero.

Applying the Zero Product Property

In our equation, we have two identical factors: (x - 4) and (x - 4). Therefore, to satisfy the equation, at least one of these factors must be equal to zero.

Step 1: Set each factor equal to zero:

  • x - 4 = 0
  • x - 4 = 0

Step 2: Solve for 'x' in each equation:

  • x = 4
  • x = 4

The Solution

We find that the solution to the equation (x - 4)(x - 4) = 0 is x = 4.

Understanding the Solution

This solution indicates that the quadratic equation has a double root at x = 4. This means that the graph of the quadratic equation touches the x-axis at the point (4, 0) and then turns around without crossing the x-axis.

In simpler terms, the equation has only one solution, but it appears twice.

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