(x+3) (x+4)=0 Quadratic Equation Answer

2 min read Jun 16, 2024

Solving the Quadratic Equation: (x+3)(x+4) = 0

This article will guide you through solving the quadratic equation (x+3)(x+4) = 0.

Understanding the Equation

The equation (x+3)(x+4) = 0 is already in a factored form. This makes solving for the values of 'x' quite straightforward.

The Zero Product Property

The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

In our equation, we have two factors: (x+3) and (x+4). The product of these factors is zero. Therefore, to satisfy the Zero Product Property, at least one of these factors must equal zero.

Solving for x

Factor 1: (x+3) = 0
- Subtract 3 from both sides: x = -3
Factor 2: (x+4) = 0
- Subtract 4 from both sides: x = -4

Solutions

Therefore, the solutions to the quadratic equation (x+3)(x+4) = 0 are:

x = -3
x = -4

Verification

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

For x = -3:
- (-3 + 3)(-3 + 4) = (0)(1) = 0
For x = -4:
- (-4 + 3)(-4 + 4) = (-1)(0) = 0

Both solutions satisfy the equation, confirming their validity.

Conclusion

By utilizing the Zero Product Property, we efficiently solved the quadratic equation (x+3)(x+4) = 0 and determined the solutions to be x = -3 and x = -4.