X^2 + 10X + 21 = 0: Explained And Solved

Graph of x^210x+21=0 from www.geteasysolution.com

Introduction:

As a professional teacher, it is important to be able to explain mathematical concepts to students in a clear and understandable way. One of the most common problems that students face in algebra is solving quadratic equations. In this article, we will explore how to solve the quadratic equation X^2 + 10x + 21 = 0.

What is a Quadratic Equation?

A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants. In this case, we have X^2 + 10x + 21 = 0. This equation is called quadratic because it contains a term with x raised to the power of two.

How to Solve a Quadratic Equation?

There are several methods to solve a quadratic equation, but one of the most common is the quadratic formula. The quadratic formula is: X = (-b ± sqrt(b^2 - 4ac)) / 2a In this formula, a, b, and c are the coefficients of the quadratic equation. To solve X^2 + 10x + 21 = 0 using the quadratic formula, we need to identify the values of a, b, and c.

Identifying the Coefficients:

In X^2 + 10x + 21 = 0, the coefficient of X^2 is 1, the coefficient of x is 10, and the constant term is 21. Therefore, a = 1, b = 10, and c = 21.

Applying the Quadratic Formula:

Now that we have identified the coefficients, we can apply the quadratic formula to solve for X. Substituting the values of a, b, and c into the formula, we get: X = (-10 ± sqrt(10^2 - 4(1)(21))) / 2(1) Simplifying this equation, we get: X = (-10 ± sqrt(100 - 84)) / 2 X = (-10 ± sqrt(16)) / 2

Simplifying the Solution:

We can further simplify the solution by finding the square root of 16, which is 4. Therefore, X = (-10 + 4) / 2 or X = (-10 - 4) / 2 Simplifying these equations, we get: X = -3 or X = -7 Therefore, the solutions to the quadratic equation X^2 + 10x + 21 = 0 are X = -3 and X = -7.

Checking the Solution:

To check whether our solution is correct, we can substitute X = -3 and X = -7 back into the original equation and see if it equals zero. When X = -3, we get: (-3)^2 + 10(-3) + 21 = 0 9 - 30 + 21 = 0 0 = 0 This confirms that X = -3 is a solution to the quadratic equation. When X = -7, we get: (-7)^2 + 10(-7) + 21 = 0 49 - 70 + 21 = 0 0 = 0 This confirms that X = -7 is also a solution to the quadratic equation.

Conclusion:

In conclusion, the quadratic equation X^2 + 10x + 21 = 0 can be solved using the quadratic formula. By identifying the coefficients and applying the formula, we found that the solutions to the equation are X = -3 and X = -7. By checking the solutions, we confirmed that they are correct. It is important for students to understand the steps involved in solving quadratic equations, as they are a fundamental part of algebra.