Understanding And Solving The Equation 2X² + 3X + 5 = 0

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Introduction

As a professional teacher, understanding and solving mathematical equations is part of your everyday life. One of the equations that students may struggle with is the quadratic equation, specifically the equation 2x² + 3x + 5 = 0. In this article, we will break down this equation and provide a step-by-step guide on how to solve it.

What is a Quadratic Equation?

A quadratic equation is a type of equation that involves a variable raised to the power of two. It is written as ax² + bx + c = 0, where a, b, and c are coefficients. The goal when solving a quadratic equation is to find the value(s) of the variable that satisfy the equation.

Breaking Down 2x² + 3x + 5 = 0

The equation 2x² + 3x + 5 = 0 is a quadratic equation, where a = 2, b = 3, and c = 5. To solve this equation, we will use the quadratic formula, which is x = (-b ± √(b² - 4ac)) / 2a.

Step 1: Identify the Coefficients

As mentioned earlier, the coefficients in this equation are a = 2, b = 3, and c = 5.

Step 2: Plug the Coefficients into the Quadratic Formula

Now that we have identified the coefficients, we can plug them into the quadratic formula to get x = (-3 ± √(3² - 4(2)(5))) / 2(2).

Step 3: Simplify the Equation

Next, we need to simplify the equation by following the order of operations. We start by simplifying the expression inside the square root: 3² - 4(2)(5) = 9 - 40 = -31. Then, we simplify the denominator by multiplying 2 by 2 to get 4.

Step 4: Find the Square Root

Now, we need to find the square root of -31. Since the square root of a negative number is not a real number, we cannot simplify it any further. Therefore, we leave it as √-31.

Step 5: Use the Quadratic Formula to Find the Solutions

Finally, we can use the quadratic formula to find the solutions: x = (-3 ± √-31) / 4. Since we cannot simplify the square root of -31, we leave the answer in this form.

Solution

In conclusion, the equation 2x² + 3x + 5 = 0 is a quadratic equation that can be solved using the quadratic formula. The solutions are x = (-3 ± √-31) / 4. As a teacher, it is important to break down complex equations like this one into smaller, more manageable steps to help students understand and solve them.