(x+1)(x+3)=0 Quadratic Equation

3 min read Jun 16, 2024

Solving the Quadratic Equation (x+1)(x+3) = 0

This article will guide you through the process of solving the quadratic equation (x+1)(x+3) = 0. We'll cover the key concepts and provide step-by-step instructions.

Understanding the Equation

The equation (x+1)(x+3) = 0 represents a quadratic equation in factored form. This form is particularly useful because it directly reveals the solutions to the equation.

Solving for x

To find the solutions for x, we utilize 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 this to our equation:

Set each factor equal to zero:
- x + 1 = 0
- x + 3 = 0
Solve for x in each equation:
- x = -1
- x = -3

Solutions

Therefore, the solutions to the quadratic equation (x+1)(x+3) = 0 are x = -1 and x = -3. These values represent the points where the graph of the quadratic function intersects the x-axis.

Verifying the Solutions

To verify our solutions, we can substitute each value of x back into the original equation:

For x = -1: (-1 + 1)(-1 + 3) = (0)(2) = 0
For x = -3: (-3 + 1)(-3 + 3) = (-2)(0) = 0

Both solutions satisfy the original equation, confirming their validity.

Conclusion

Solving the quadratic equation (x+1)(x+3) = 0 is a straightforward process that demonstrates the power of factoring and the Zero Product Property. This approach allows us to efficiently find the solutions and understand their significance in the context of the equation.