(2x+7)(x-1)=0 Quadratic Equation

2 min read Jun 16, 2024

Solving the Quadratic Equation: (2x+7)(x-1) = 0

This article will guide you through solving the quadratic equation (2x+7)(x-1) = 0.

Understanding the Zero Product Property

The equation (2x+7)(x-1) = 0 is already in a factored form. This form is particularly useful because it allows us to apply the Zero Product Property. This property states:

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 to Solve the Equation

Set each factor equal to zero:
- 2x + 7 = 0
- x - 1 = 0
Solve each equation for x:
- 2x + 7 = 0
  - 2x = -7
  - x = -7/2
- x - 1 = 0
  - x = 1

Solutions

Therefore, the solutions to the quadratic equation (2x+7)(x-1) = 0 are:

x = -7/2
x = 1

Verifying the Solutions

You can always verify your solutions by plugging them back into the original equation:

For x = -7/2:
- (2(-7/2) + 7)(-7/2 - 1) = 0
- (0)(-9/2) = 0
- 0 = 0 (This confirms that x = -7/2 is a valid solution)
For x = 1:
- (2(1) + 7)(1 - 1) = 0
- (9)(0) = 0
- 0 = 0 (This confirms that x = 1 is a valid solution)

Conclusion

The quadratic equation (2x+7)(x-1) = 0 has two solutions: x = -7/2 and x = 1. By using the Zero Product Property, we could efficiently solve the equation and verify our answers.