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(x-4)(x-7)=0

less than a minute read Jun 17, 2024
(x-4)(x-7)=0

Solving the Equation (x-4)(x-7) = 0

This equation is a simple quadratic equation in factored form. To solve it, we can use the Zero Product Property. This property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Applying the Zero Product Property

  1. Set each factor equal to zero:

    • x - 4 = 0
    • x - 7 = 0

  2. Solve for x in each equation:

    • x = 4
    • x = 7

Solution

Therefore, the solutions to the equation (x-4)(x-7) = 0 are x = 4 and x = 7.

Verification

We can verify our solutions by plugging them back into the original equation:

  • For x = 4: (4 - 4)(4 - 7) = 0 * -3 = 0 (True)
  • For x = 7: (7 - 4)(7 - 7) = 3 * 0 = 0 (True)

This confirms that our solutions are correct.

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