(x%2B4)%3D0-in-standard-form.jpeg "(x+5)(x+4)=0 In Standard Form")
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.