-(x%2B4)%3D0-quadratic-equation-in-standard-form.jpeg "(x+3) (x+4)=0 Quadratic Equation In Standard Form")
Solving the Quadratic Equation (x+3)(x+4) = 0
This article will guide you through solving the quadratic equation (x+3)(x+4) = 0 and understanding the process of converting it to standard form.
Understanding the Equation
The equation (x+3)(x+4) = 0 is already factored. This means it's in a form that makes it easy to find the solutions.
Key Concept: For a product of two or more factors to equal zero, at least one of the factors must be zero.
Solving for x
To find the solutions, we set each factor equal to zero:
- x + 3 = 0
- Subtract 3 from both sides: x = -3
- x + 4 = 0
- Subtract 4 from both sides: x = -4
Therefore, the solutions to the quadratic equation (x+3)(x+4) = 0 are x = -3 and x = -4.
Standard Form of a Quadratic Equation
The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
To convert the given equation to standard form, we need to expand the product:
(x+3)(x+4) = 0
- x² + 4x + 3x + 12 = 0
- x² + 7x + 12 = 0
Now the equation is in standard form: x² + 7x + 12 = 0.
Conclusion
We have successfully solved the quadratic equation (x+3)(x+4) = 0 by using the factored form to find the solutions: x = -3 and x = -4. We also converted the equation to standard form: x² + 7x + 12 = 0. This process demonstrates the relationship between factored and standard forms of quadratic equations and how they can be used to solve for the roots.