Explanation And Solution Of "X^2 + 2X + 2X + 0"

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Introduction

As a professional teacher, I understand that math can be a challenging subject for many students. Therefore, it is important to break down problems and provide clear explanations and solutions. In this article, we will be discussing the equation "x^2 + 2x + 2x + 0" and how to solve it.

The Equation

The equation "x^2 + 2x + 2x + 0" is a quadratic equation. This means that the highest exponent in the equation is 2. The equation can also be written as "x^2 + 4x + 0", since 2x + 2x is equal to 4x.

Simplifying the Equation

Before we can solve the equation, we need to simplify it as much as possible. In this case, we can simplify the equation by combining the like terms. 2x + 2x is equal to 4x, so we can rewrite the equation as "x^2 + 4x + 0".

Solving the Equation

To solve the equation, we need to find the values of x that make the equation true. We can do this by factoring the equation, completing the square, or using the quadratic formula.

Factoring the Equation

To factor the equation "x^2 + 4x + 0", we need to find two numbers that multiply to 0 and add to 4. The only two numbers that satisfy this condition are 0 and 4. Therefore, we can factor the equation as "x(x + 4) = 0". This means that either x or x + 4 is equal to 0. Solving for x, we get x = 0 or x = -4.

Completing the Square

To complete the square for the equation "x^2 + 4x + 0", we need to add and subtract a constant to the equation. The constant we need to add is (4/2)^2, which is equal to 4. We can rewrite the equation as "x^2 + 4x + 4 - 4 = 0". The first three terms can be factored as (x + 2)^2, so we can rewrite the equation as "(x + 2)^2 - 4 = 0". Solving for x, we get x = -2 + 2 or x = -2 - 2, which gives us x = 0 or x = -4.

Using the Quadratic Formula

The quadratic formula is another method we can use to solve the equation "x^2 + 4x + 0". The quadratic formula is x = (-b ± sqrt(b^2 - 4ac)) / 2a, where a, b, and c are the coefficients of the equation. In this case, a = 1, b = 4, and c = 0. Plugging these values into the quadratic formula, we get x = (-4 ± sqrt(4^2 - 4(1)(0))) / 2(1), which simplifies to x = (-4 ± sqrt(16)) / 2. Solving for x, we get x = -2 or x = 0.

Conclusion

In conclusion, the equation "x^2 + 2x + 2x + 0" can be simplified to "x^2 + 4x + 0". We can solve the equation by factoring, completing the square, or using the quadratic formula. The solutions to the equation are x = 0 or x = -4. As a teacher, it is important to provide clear explanations and solutions to help students understand and succeed in math.