Solving Quadratic Equations: X²+4X=0

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Introduction

Quadratic equations are equations that have the form ax²+bx+c=0, where a, b, and c are constants. Solving quadratic equations involves finding the values of x that satisfy the equation. In this article, we will discuss how to solve the quadratic equation x²+4x=0.

Understanding the Equation

The equation x²+4x=0 is a quadratic equation in its standard form. This means that the highest power of x is 2. To solve this equation, we need to find the values of x that make the equation true. In other words, we need to find the values of x that satisfy the equation.

Factoring the Equation

One way to solve the equation x²+4x=0 is to factor it. To factor the equation, we need to find two values that multiply to give us 0. In this case, we can see that x(x+4)=0. This means that either x=0 or x+4=0. Solving for x, we get x=0 or x=-4.

Using the Quadratic Formula

Another way to solve the equation x²+4x=0 is to use the quadratic formula. The quadratic formula is x=(-b±√(b²-4ac))/2a. In this equation, a=1, b=4, and c=0. Plugging these values into the formula, we get x=(-4±√(4²-4(1)(0)))/2(1). Simplifying this equation, we get x=(-4±2√4)/2, which simplifies further to x=-2 or x=0.

Conclusion

In conclusion, the equation x²+4x=0 can be solved by factoring or by using the quadratic formula. Factoring the equation gives us x=0 or x=-4, while using the quadratic formula gives us x=-2 or x=0. It is important to note that quadratic equations can have complex solutions, and that there are many methods for solving these equations.