-(x%2B4)%3D0-quadratic-equation.jpeg "(x+3) (x+4)=0 Quadratic Equation")
(x+3)(x+4)=0: Solving a Quadratic Equation
In algebra, a quadratic equation is a polynomial equation of degree two, which means the highest power of the variable (usually x) is two. The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants. In this article, we will focus on the specific quadratic equation (x+3)(x+4)=0 and learn how to solve it.
Factoring the Equation
The given equation is already in factored form, which makes it easier to solve. The equation can be written as:
(x+3)(x+4) = 0
This tells us that either (x+3) = 0 or (x+4) = 0.
Solving for x
To find the values of x, we set each factor equal to zero and solve for x:
(x+3) = 0 x + 3 = 0 x = -3
(x+4) = 0 x + 4 = 0 x = -4
Therefore, the solutions to the equation (x+3)(x+4)=0 are x = -3 and x = -4.
Graphical Representation
The graph of the equation (x+3)(x+4)=0 is a parabola that opens upward. The x-intercepts of the graph are the solutions we found earlier, x = -3 and x = -4. The graph will cross the x-axis at these points.
Real-World Applications
Quadratic equations like (x+3)(x+4)=0 have many real-world applications, such as:
- Projectile motion: The trajectory of a projectile under gravity can be modeled using quadratic equations.
- Optimization problems: Quadratic equations are used to solve optimization problems, such as finding the maximum or minimum value of a function.
- Electric circuits: Quadratic equations are used to analyze and design electric circuits.
In conclusion, the equation (x+3)(x+4)=0 is a simple quadratic equation that can be easily solved by factoring. The solutions to the equation are x = -3 and x = -4, which can be represented graphically as the x-intercepts of a parabola. Quadratic equations have many real-world applications, and understanding how to solve them is an important skill in algebra and beyond.
