## Solving Quadratic Equations in Standard Form: (x + 5)(x + 4) = 0

This article explores how to solve the quadratic equation (x + 5)(x + 4) = 0 and express it in standard form.

### Understanding the Equation

The equation (x + 5)(x + 4) = 0 represents a quadratic equation in factored form. This form highlights the roots or solutions of the equation, which are the values of x that make the equation true.

### Solving for x

To find the solutions, we can use the **Zero Product Property**:

**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:

**(x + 5) = 0**or**(x + 4) = 0**

Solving for x in each case:

**x = -5**or**x = -4**

Therefore, the solutions to the equation (x + 5)(x + 4) = 0 are **x = -5** and **x = -4**.

### Standard Form of the Equation

The standard form of a quadratic equation is **ax² + bx + c = 0**, where a, b, and c are constants.

To express our equation in standard form, we need to expand the factored form and simplify:

**Expand the product:**(x + 5)(x + 4) = x² + 4x + 5x + 20**Combine like terms:**x² + 9x + 20 = 0

Therefore, the standard form of the equation (x + 5)(x + 4) = 0 is **x² + 9x + 20 = 0**.

### Conclusion

We have successfully solved the quadratic equation (x + 5)(x + 4) = 0, finding its roots to be x = -5 and x = -4. We also converted the equation to its standard form, x² + 9x + 20 = 0. This process demonstrates the importance of understanding different forms of quadratic equations and how to manipulate them to solve for unknown variables.