The Quadratic Equation: X² + 2X + 15 = 0

X2+2x15=0 cuanto es y cómo se hace Brainly.lat from brainly.lat

Introduction

As a professional teacher, it is my duty to explain and solve the quadratic equation: x² + 2x + 15 = 0. This equation is a quadratic polynomial, which means it has a degree of two. To solve this equation, we need to find the values of x that make it true.

The Quadratic Formula

One way to solve the quadratic equation is by using the quadratic formula. The quadratic formula is: x = (-b ± √(b² - 4ac)) / 2a, where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1, b = 2, and c = 15.

Step-by-Step Solution using Quadratic Formula

Now let us use the quadratic formula to solve the equation x² + 2x + 15 = 0.

Step 1: Identify the values of a, b, and c in the equation.

a = 1, b = 2, c = 15

Step 2: Substitute the values of a, b, and c into the quadratic formula.

x = (-2 ± √(2² - 4(1)(15))) / 2(1)

Step 3: Simplify the equation.

x = (-2 ± √(-56)) / 2

x = (-2 ± 2i√14) / 2

x = -1 ± i√14

Solution

Therefore, the solution to the equation x² + 2x + 15 = 0 is x = -1 ± i√14. This means that there are no real solutions to the equation, but there are two complex solutions.

Conclusion

Solving quadratic equations is an important skill in mathematics. The quadratic formula is a useful tool for finding the solutions of quadratic equations, especially when factoring is not possible. In this case, we used the quadratic formula to find the complex solutions of the equation x² + 2x + 15 = 0.