(2x+7)(2x-7)=0

2 min read Jun 16, 2024

Solving the Equation (2x + 7)(2x - 7) = 0

This equation is a simple example of a quadratic equation that can be solved using 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

Identify the factors: In our equation, the factors are (2x + 7) and (2x - 7).
Set each factor equal to zero:
- 2x + 7 = 0
- 2x - 7 = 0
Solve for x in each equation:
- For 2x + 7 = 0:
  - Subtract 7 from both sides: 2x = -7
  - Divide both sides by 2: x = -7/2
- For 2x - 7 = 0:
  - Add 7 to both sides: 2x = 7
  - Divide both sides by 2: x = 7/2

Solutions

Therefore, the solutions to the equation (2x + 7)(2x - 7) = 0 are x = -7/2 and x = 7/2.

Verification

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

For x = -7/2:
- (2*(-7/2) + 7)(2*(-7/2) - 7) = (0)(-14) = 0
For x = 7/2:
- (2*(7/2) + 7)(2*(7/2) - 7) = (14)(0) = 0

Both solutions satisfy the original equation.

Conclusion

By applying the Zero Product Property, we successfully solved the quadratic equation (2x + 7)(2x - 7) = 0, obtaining the solutions x = -7/2 and x = 7/2. This demonstrates a straightforward method for solving equations of this type.