Solving X In 2X<Sup>2</Sup> + 16X + 9 = 0

Ex 6.1, 16 Solve (2x 1)/3 >= (3x 2)/4 (2 x)/5 from www.teachoo.com

Introduction

If you are looking for a way to solve the equation 2x² + 16x + 9 = 0, then you have come to the right place. This equation is known as a quadratic equation, which means it has a degree of 2. Solving quadratic equations is a fundamental skill in algebra and is used in many fields such as physics, engineering, and economics.

Understanding Quadratic Equations

Before we dive into solving the equation, let's first understand what a quadratic equation is. A quadratic equation is an equation in which the highest power of the variable is 2. In general, a quadratic equation can be written in the form ax² + bx + c = 0, where a, b, and c are constants.

The Quadratic Formula

One of the most common methods for solving quadratic equations is by using the quadratic formula, which is: x = (-b ± √(b² - 4ac)) / 2a In this equation, x represents the solution to the quadratic equation, and a, b, and c are the coefficients of the quadratic equation. The ± symbol means that there are two possible solutions, one with a plus sign and one with a minus sign.

Solving the Quadratic Equation

Now that we understand the quadratic formula, let's use it to solve the equation 2x² + 16x + 9 = 0. First, we need to identify the coefficients of the quadratic equation: a = 2 b = 16 c = 9 We can now plug these values into the quadratic formula and simplify: x = (-16 ± √(16² - 4(2)(9))) / 2(2) x = (-16 ± √(256 - 72)) / 4 x = (-16 ± √184) / 4 x = (-16 ± 2√46) / 4 x = -4 ± (1/2)√46

Final Solution

Therefore, the solutions to the quadratic equation 2x² + 16x + 9 = 0 are: x = -4 + (1/2)√46 x = -4 - (1/2)√46

Conclusion

In conclusion, solving quadratic equations is a crucial skill in algebra, and the quadratic formula is a powerful tool for finding the solutions to these types of equations. By using the quadratic formula, we were able to find the solutions to the equation 2x² + 16x + 9 = 0. Remember, practice makes perfect, so keep practicing and solving quadratic equations, and soon you will be an expert!