(x+7)(x+4)=0

2 min read Jun 17, 2024

Solving the Equation: (x+7)(x+4) = 0

This equation represents a quadratic equation in factored form. To solve it, we utilize the Zero Product Property, which 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

Set each factor equal to zero:
- x + 7 = 0
- x + 4 = 0
Solve for x in each equation:
- x = -7
- x = -4

The Solution

Therefore, the solutions to the equation (x + 7)(x + 4) = 0 are x = -7 and x = -4.

This means that if you substitute either -7 or -4 for 'x' in the original equation, the equation will be true.

Visualizing the Solution

Graphically, the solutions represent the x-intercepts of the parabola represented by the quadratic equation. The parabola crosses the x-axis at the points (-7, 0) and (-4, 0).

Conclusion

By applying the Zero Product Property, we can efficiently solve factored quadratic equations like (x + 7)(x + 4) = 0. This method provides a straightforward way to find the values of x that make the equation true.