X^2 + 7X + 6 = 0: Explanation And Solution

найдите произведение корней уравнения x^27x+6=0 Школьные from znanija.com

Introduction

As a professional teacher, it is essential to help students understand complex mathematical concepts. One of these concepts is solving quadratic equations, such as X^2 + 7x + 6 = 0. This equation is a quadratic equation, which is an equation that contains variables with exponents of two. The equation has an unknown variable (X) that we need to solve for. In this article, we will explain how to solve this equation and provide a step-by-step solution.

Understanding Quadratic Equations

Quadratic equations are mathematical expressions that contain variables raised to the power of two. These expressions are in the form of ax^2 + bx + c = 0, where x is the variable, a, b, and c are constants. In the equation X^2 + 7x + 6 = 0, a=1, b=7, and c=6. To solve this equation, we need to find the value of x that satisfies the equation.

The Quadratic Formula

The quadratic formula is a standard formula used to solve quadratic equations. It is in the form of (-b ± √(b^2 - 4ac))/(2a). Using this formula, we can solve any quadratic equation, including X^2 + 7x + 6 = 0.

Solving for X

To solve the equation X^2 + 7x + 6 = 0, we need to use the quadratic formula. First, we need to identify the values of a, b, and c. In this equation, a=1, b=7, and c=6. We can plug these values into the quadratic formula and simplify the equation.

Step 1:

Identify the values of a, b, and c in the equation ax^2 + bx + c = 0. In this equation, a=1, b=7, and c=6.

Step 2:

Plug the values of a, b, and c into the quadratic formula: (-b ± √(b^2 - 4ac))/(2a)

Step 3:

Simplify the equation: (-7 ± √(7^2 - 4(1)(6)))/(2(1))

Step 4:

Simplify the equation further: (-7 ± √(49 - 24))/2

Step 5:

Simplify the equation: (-7 ± √25)/2

Step 6:

Simplify the equation further: (-7 ± 5)/2

Step 7:

Simplify the equation: X1 = (-7 + 5)/2 = -1 and X2 = (-7 - 5)/2 = -6

Conclusion

In conclusion, the equation X^2 + 7x + 6 = 0 is a quadratic equation that can be solved using the quadratic formula. The solution to this equation is X1= -1 and X2= -6. As a professional teacher, it is essential to help students understand the steps involved in solving quadratic equations. By breaking down the process into simple steps, students can easily solve complex mathematical problems.