Unraveling the Mystery: Finding the Value of x in -x² = 81

In this article, we will delve into the mystery of finding the value of x in the equation -x² = 81. Solving quadratic equations can sometimes be challenging, but fear not, as we will break down the process step by step to help you understand and unlock the solution.

Understanding the Quadratic Equation -x² = 81

Before we dive into solving the equation -x² = 81, it’s essential to understand the basics of quadratic equations. A quadratic equation is a polynomial equation of the second degree, which means the highest power of the variable is 2. In this case, the equation -x² = 81 is a quadratic equation where the variable x is squared and multiplied by -1.

Step-by-Step Solution Process

Now let’s unravel the mystery and find the value of x in the equation -x² = 81. We will follow a step-by-step process to solve this quadratic equation:

Step 1: Move -x² to the Right Side

The first step is to move -x² to the right side of the equation to isolate x². By adding x² to both sides, the equation becomes x² = -81.

Step 2: Take the Square Root

Next, we take the square root of both sides of the equation to solve for x. The square root of x² is x, and the square root of -81 is ±9i, where i is the imaginary unit.

Step 3: Finalizing the Solution

Since x can be expressed as ±9i, the final solution to the equation -x² = 81 is x = ±9i. In this case, x can take on two complex values, which are ±9i.

FAQs

Q: Can x have real values in the equation -x² = 81?

A: No, in the equation -x² = 81, x can only have complex values.

Q: Why do we take the square root in the solution process?

A: Taking the square root helps us isolate x and find the possible values of x in the equation.

Q: Is it possible to have multiple solutions for x in a quadratic equation?

A: Yes, quadratic equations can have one, two, or even no real solutions depending on the nature of the equation.

Q: Can the value of x in -x² = 81 be simplified further?

A: The value of x = ±9i in -x² = 81 is already in its simplest form as complex numbers.

Q: How can we verify the solution of x = ±9i in the equation?

A: Plug in the values of x = ±9i back into the original equation to check if they satisfy the equation -x² = 81.

Conclusion

In conclusion, we have successfully unraveled the mystery of finding the value of x in the equation -x² = 81. By following the step-by-step solution process, we have discovered that x can take on the complex values of ±9i. Quadratic equations may seem daunting at first, but with practice and understanding, solving them can become more manageable. Remember to approach each equation methodically and break it down into simpler steps to find the desired solution. With determination and perseverance, you can conquer any quadratic equation that comes your way.