Solving Quadratic Equations: X² + 4X + 21 = 0

X2+4X21=0 Quadratic Equation By Completing The Square Nosdevoirs from fr.youtubemoney.co

Introduction

In mathematics, a quadratic equation is a polynomial equation of the second degree. It involves the variable x, and the equation can be written in the form ax² + bx + c = 0, where a, b, and c are constants. In this article, we will be discussing how to solve the quadratic equation x² + 4x + 21 = 0.

Understanding Quadratic Equations

A quadratic equation is an equation of the form ax² + bx + c = 0. The term "quadratic" comes from the Latin word "quadratus," which means "square." This is because the variable x is squared in the equation. Quadratic equations have two solutions, which can be real or complex numbers.

Solving Quadratic Equations

To solve a quadratic equation, we need to find the values of x that make the equation true. There are several methods for solving quadratic equations, including factoring, completing the square, and using the quadratic formula. In this article, we will be using the quadratic formula to solve x² + 4x + 21 = 0.

The Quadratic Formula

The quadratic formula is a formula that gives the solutions of a quadratic equation in terms of its coefficients. The formula is: x = (-b ± √(b² - 4ac)) / 2a In this formula, a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0. The symbol ± means that we need to find both the positive and negative solutions.

Applying the Quadratic Formula

Let's apply the quadratic formula to solve x² + 4x + 21 = 0. In this equation, a = 1, b = 4, and c = 21. Substituting these values into the quadratic formula, we get: x = (-4 ± √(4² - 4(1)(21))) / 2(1) Simplifying the expression inside the square root, we get: x = (-4 ± √(-68)) / 2 The expression inside the square root is negative, which means that the solutions of the quadratic equation are complex numbers. We can simplify the expression further by using the imaginary unit i, which is defined as √(-1). Therefore, we have: x = (-4 ± i√68) / 2 Simplifying the expression, we get: x = -2 ± 2i√17 Therefore, the solutions of the quadratic equation x² + 4x + 21 = 0 are: x = -2 + 2i√17 and x = -2 - 2i√17

Conclusion

In conclusion, solving quadratic equations is an important skill in mathematics. In this article, we have discussed how to solve the quadratic equation x² + 4x + 21 = 0 using the quadratic formula. We have also learned that the solutions of the quadratic equation can be real or complex numbers. By understanding the quadratic formula and its application, students can solve a wide range of quadratic equations and apply this knowledge to real-world problems.