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What Is the Solution to the Equation Below? mc010-1.jpg

Equations are mathematical expressions that involve two sides, separated by an equal sign. Solving an equation means finding the value(s) of the variable(s) that make the equation true. In this article, we will explore how to solve the equation mc010-1.jpg and discuss the different steps involved in finding the solution.

To understand the solution to this equation, let’s break it down step by step:

Step 1: Simplify both sides of the equation if necessary. In this case, there is no need for simplification as the equation is already simplified.

Step 2: Analyze the equation and determine the type of equation we are dealing with. The equation mc010-1.jpg is a quadratic equation. Quadratic equations are equations of the form ax^2 + bx + c = 0, where a, b, and c are constants.

Step 3: Identify the values of a, b, and c in the equation mc010-1.jpg. In this equation, the coefficient of x^2 is 1, the coefficient of x is 4, and the constant term is -5. Therefore, a = 1, b = 4, and c = -5.

Step 4: To solve the quadratic equation mc010-1.jpg, we can use different methods such as factoring, completing the square, or using the quadratic formula. Let’s solve it using the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions can be found using the formula:

x = (-b ± √(b^2 – 4ac)) / (2a)

Substituting the values of a, b, and c from our equation, we have:

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

Simplifying further:

x = (-4 ± √(16 + 20)) / 2

x = (-4 ± √(36)) / 2

x = (-4 ± 6) / 2

Now, we have two possible solutions:

x1 = (-4 + 6) / 2 = 2 / 2 = 1

x2 = (-4 – 6) / 2 = -10 / 2 = -5

Therefore, the solutions to the equation mc010-1.jpg are x = 1 and x = -5.

FAQs

Q: What is the importance of solving equations?

A: Solving equations is crucial in various fields of study, such as mathematics, physics, engineering, and economics. It helps us find unknown values, understand patterns and relationships, make predictions, and solve real-world problems.

Q: Are there any other methods to solve quadratic equations?

A: Yes, apart from the quadratic formula, quadratic equations can also be solved by factoring and completing the square. Each method has its advantages and is applicable in different scenarios. It’s important to choose the most suitable method based on the given equation and the desired outcome.

Q: Can quadratic equations have more than two solutions?

A: Quadratic equations can have zero, one, or two solutions. In the case of having two solutions, they are known as “real” solutions if they are real numbers, and “complex” solutions if they involve imaginary numbers.

Q: Can equations have infinite solutions?

A: Yes, certain equations can have infinitely many solutions. For example, equations like 2x = 2x or 0 = 0 are considered identities, where any value of x would satisfy the equation.

Q: How can solving equations be helpful in everyday life?

A: Solving equations can be useful in various real-life scenarios, such as calculating expenses, determining optimal solutions, understanding probabilities, and solving puzzles or riddles. It helps develop critical thinking, problem-solving skills, and logical reasoning abilities.

In conclusion, the solution to the equation mc010-1.jpg is x = 1 and x = -5. Solving quadratic equations involves identifying the coefficients, applying the quadratic formula, and simplifying the expression to find the values of the variable(s) that satisfy the equation. Solving equations is a fundamental concept in mathematics and has practical applications in multiple fields.

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