Solving The Mystery: – 2 – 5X – 12 Explained

Are you struggling to solve the equation – 2 – 5x – 12? Well, you’ve come to the right place! In this article, we will dive into the world of algebraic equations and uncover the solution to this particular problem. No need to fear, we’ll break it down step by step, making it easy to follow along. So, let’s jump right in and conquer – 2 – 5x – 12 together!

Solving the Mystery: - 2 - 5x - 12 Explained

– 2 – 5x – 12: Understanding the Quadratic Equation

Introduction

In the world of mathematics, quadratic equations hold a significant place. One such equation, – 2 – 5x – 12, is a common example encountered in algebra classes. Understanding how to solve this equation can unlock the door to solving a wide range of quadratic equations. In this comprehensive guide, we will dive deep into the intricacies of – 2 – 5x – 12 and explore various techniques to solve it. So, let’s embark on this mathematical journey together!

What is a Quadratic Equation?

Before diving into the specifics of – 2 – 5x – 12, let’s take a moment to understand what a quadratic equation is. A quadratic equation is a second-degree polynomial equation, typically written in the form ax^2 + bx + c = 0. The exponents of the variable x determine its degree. In this case, the exponents are raised to the power of 2, making it a quadratic equation.

Understanding the Components: – 2 – 5x – 12

To begin deciphering this quadratic equation, let’s break it down into its components:

  • Constant term (-2): The constant term is a number that stands alone, without any variable attached to it. In this equation, -2 represents the constant term.
  • Linear term (-5x): A linear term consists of a variable (x) multiplied by a coefficient (-5 in this case). It is called a linear term because the exponent of x is 1, making it a first-degree term.
  • Quadratic term (-12): The quadratic term consists of a variable (x) raised to the power of 2, making it a second-degree term. -12 represents the quadratic term in this equation.

Solving the Quadratic Equation

Now that we have familiarized ourselves with the components of – 2 – 5x – 12, let’s explore the techniques to solve it.

1. Factoring Method

Factoring is one of the most commonly used methods to solve quadratic equations. To solve – 2 – 5x – 12 using factoring, follow these steps:

  1. Set the equation equal to zero: – 2 – 5x – 12 = 0
  2. Factor the quadratic equation: (x + 2)(5x + 6) = 0
  3. Apply the zero-product property: x + 2 = 0 or 5x + 6 = 0
  4. Solve the linear equations: x = -2 or x = -6/5

By employing the factoring method, we have successfully found the two possible solutions for the quadratic equation – 2 – 5x – 12, which are x = -2 and x = -6/5.

2. Quadratic Formula

Another powerful technique to solve quadratic equations is by using the quadratic formula. The quadratic formula is derived from completing the square and is expressed as:

x = (-b ± √(b^2 – 4ac)) / (2a)

To solve – 2 – 5x – 12 using the quadratic formula, let’s identify the corresponding coefficients:

  • a = -5
  • b = -1
  • c = -12

Substituting these values into the quadratic formula, we have:

x = (-(-1) ± √((-1)^2 – 4(-5)(-12))) / (2(-5))

Simplifying further, we get:

x = (1 ± √(1 – 240)) / (-10)

After simplification, we have two possible solutions for x:

  • x = (1 + √239) / -10
  • x = (1 – √239) / -10

3. Completing the Square

Completing the square is yet another technique to solve quadratic equations, especially when factoring becomes challenging. Here’s how you can solve – 2 – 5x – 12 using the completing the square method:

  1. Set the equation equal to zero: – 2 – 5x – 12 = 0
  2. Rearrange the equation: x^2 + 5x + 10 = 0
  3. Complete the square by adding the square of half the coefficient of x:
    (x + 5/2)^2 – (5/2)^2 + 10 = 0
  4. Simplify and rearrange: (x + 5/2)^2 = 5/4
  5. Take the square root of both sides: x + 5/2 = ±√(5/4)
  6. Solve for x: x = -5/2 ± √(5/4)

Upon solving, we find the two possible solutions for x:

  • x = -5/2 + √(5/4)
  • x = -5/2 – √(5/4)

In this comprehensive guide, we have delved into the world of quadratic equations with a specific focus on – 2 – 5x – 12. By understanding the components of this equation and utilizing various techniques such as factoring, the quadratic formula, and completing the square, we have successfully solved for the value(s) of x. Quadratic equations form the foundation for many mathematical concepts, and by mastering them, you will be equipped to tackle more complex problems in algebra and beyond. So, embrace the power of quadratic equations and unleash your mathematical prowess!

FACTORISE , FACTORISATION 2𝑥^2+ 5𝑥 −12

Frequently Asked Questions

What is the expression -2 – 5x – 12?

The expression -2 – 5x – 12 represents a mathematical expression involving the variable ‘x’. It can be simplified or evaluated by substituting a value for ‘x’ and performing the necessary arithmetic operations.

How can I simplify the expression -2 – 5x – 12?

To simplify the expression -2 – 5x – 12, you can combine like terms. In this case, the like terms are the coefficients of ‘x’. Combining -5x and -12, we get -5x – 12. Finally, adding -2 to -5x – 12 gives us the simplified expression -5x – 14.

Can the expression -2 – 5x – 12 be solved?

The expression -2 – 5x – 12 is not an equation, but rather an algebraic expression. As such, it cannot be “solved” in the traditional sense. However, it can be simplified or evaluated by substituting specific values for ‘x’.

What does the variable ‘x’ represent in the expression -2 – 5x – 12?

In the expression -2 – 5x – 12, the variable ‘x’ represents an unknown quantity or a variable that can take on different values. It is commonly used in algebraic equations and expressions to denote an unknown value that needs to be determined or evaluated.

Is there a specific range of values for ‘x’ in the expression -2 – 5x – 12?

No, there is no specific range of values for ‘x’ in the expression -2 – 5x – 12 unless specified in a given context or when solving a particular problem. ‘x’ can take on any real number value unless otherwise stated or restricted by a specific condition or equation.

Can I substitute values for ‘x’ in the expression -2 – 5x – 12?

Yes, you can substitute values for ‘x’ in the expression -2 – 5x – 12. By replacing ‘x’ with a specific number, you can evaluate the expression and obtain a numerical result. This can be useful for solving equations or simplifying expressions in various mathematical problems.

Final Thoughts

– 2 – 5x – 12 is an algebraic expression that represents a mathematical equation. By simplifying this expression, we can determine its value or form a solution. It is essential to understand the steps involved in simplifying such equations to accurately solve mathematical problems. By breaking down the expression into its constituent parts and applying the appropriate mathematical operations, we can determine the final value. Whether you are a student or someone who needs to solve equations regularly, understanding the process of simplifying expressions like – 2 – 5x – 12 can greatly enhance your mathematical skills.