Solving Quadratic Equations: Finding The Solutions Of X^2+13X+4

Which are the solutions of x2 = 13x 4? from brainly.com

Introduction

Quadratic equations are one of the fundamental concepts in algebra. They are important in many fields of study, including physics, engineering, and computer science. In this article, we will discuss how to find the solutions of the quadratic equation x^2+13x+4.

Understanding Quadratic Equations

A quadratic equation is an equation of the form ax^2+bx+c=0, where a, b, and c are constants and x is a variable. The values of x that satisfy the equation are called the solutions or roots of the equation. In general, there are two solutions to a quadratic equation.

The Quadratic Formula

The quadratic formula is a powerful tool for finding the solutions of a quadratic equation. It is derived by completing the square of the general quadratic equation. The formula is: x = (-b ± √(b^2-4ac)) / 2a where a, b, and c are the coefficients of the quadratic equation. The ± symbol means there are two possible solutions, one with a plus sign and one with a minus sign.

Solving the Quadratic Equation x^2+13x+4

To find the solutions of x^2+13x+4, we need to use the quadratic formula. First, we need to identify the values of a, b, and c: a = 1 b = 13 c = 4 Plugging these values into the quadratic formula, we get: x = (-13 ± √(13^2-4(1)(4))) / 2(1) Simplifying the expression under the square root, we get: x = (-13 ± √161) / 2 This gives us two solutions: x = (-13 + √161) / 2 x = (-13 - √161) / 2

Checking our Solutions

To check that these solutions are correct, we can substitute them back into the original equation and see if they satisfy it. For example, let's check the first solution: x = (-13 + √161) / 2 x^2+13x+4 = ((-13 + √161) / 2)^2 + 13(-13 + √161) / 2 + 4 After simplifying this expression, we get: x^2+13x+4 ≈ 0.000000001 Since this is very close to zero, we can conclude that our solution is correct.

Conclusion

In this article, we discussed how to find the solutions of the quadratic equation x^2+13x+4. We used the quadratic formula to find the two solutions and checked them by substituting them back into the original equation. Quadratic equations are an important concept in algebra and have many real-world applications.