(x-8)(2x+5)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-8)(2x+5) = 0

This equation represents a quadratic expression in factored form. To solve for x, we can use the Zero Product Property:

Zero Product Property: If the product of two or more factors is zero, then at least one of the factors must be zero.

Applying this to our equation:

• Factor 1: (x-8)
• Factor 2: (2x+5)

For the product to equal zero, either (x-8) must equal zero, or (2x+5) must equal zero.

Solving for x:

1. Case 1: (x-8) = 0 Adding 8 to both sides, we get: x = 8

2. Case 2: (2x+5) = 0 Subtracting 5 from both sides: 2x = -5 Dividing both sides by 2: x = -5/2

Therefore, the solutions to the equation (x-8)(2x+5) = 0 are x = 8 and x = -5/2.

Checking our solutions:

We can substitute each solution back into the original equation to verify if it holds true.

• For x = 8: (8-8)(2(8)+5) = 0 * 21 = 0 (True)

• For x = -5/2: (-5/2 - 8)(2(-5/2) + 5) = (-21/2)(0) = 0 (True)

Conclusion:

The solutions x = 8 and x = -5/2 satisfy the equation (x-8)(2x+5) = 0. We have successfully solved the equation using the Zero Product Property.