Problem 64 \(z^{2}=-z^{2}\)... [FREE SOLUTION]

91影视

Chapter 2: Problem 64

\(z^{2}=-z^{2}\)

Short Answer

Expert verified

z = 0

Step by step solution

Set Up the Equation

Start with the given equation: \[z^{2} = -z^{2}\]

Combine Like Terms

Move all terms to one side of the equation to set it to zero. Add \(z^{2}\) to both sides: \[z^{2} + z^{2} = 0\]

Simplify

Combine the terms on the left side: \[2z^{2} = 0\]

Solve for z

Divide both sides of the equation by 2: \[z^{2} = 0\] Now take the square root of both sides: \[z = 0\]

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Equation Solving

Solving equations is a foundational skill in algebra. The goal is to find the value of the variable that makes the equation true.
For example, in the equation given: \(z^{2} = -z^{2}\), you want to isolate the variable z to find its value.
Remember these steps:

Move all terms to one side: This makes it easier to simplify the equation.
Simplify the equation: Combine like terms to get a simpler expression to work with.
Isolate the variable: Perform operations to solve for the unknown.

These steps can help you solve more complex equations as well.

Combining Like Terms

Combining like terms is a method to simplify equations. This means adding or subtracting terms with the same variable and exponent.
In our exercise, we combined the terms \(z^{2} + z^{2}\) to get \(2z^{2} = 0\).
When you have terms like \(3x\) and \(5x\), combining them gives \(8x\). Similarly, \(2y^{2} - y^{2}\) simplifies to \(y^{2}\).
This step is crucial before isolating the variable because it makes the equation simpler and easier to solve. Remember: always work with like terms to make the algebra easier.

Square Roots

Taking the square root of both sides is a common method for solving equations that involve squares.
In our exercise, after simplifying to \(z^{2} = 0\), we took the square root of both sides to find \(z\).
Remember: The square root function reverses the squaring operation. The square root of \(a^{2}\) is \(a\). For example, \(\sqrt{16} = 4\) because \(4^{2} = 16\).

When you take the square root of both sides, don鈥檛 forget about the \(\backslash \pm\) symbol for potential negative roots, but here it's not applicable since 0 has only one square root, which is 0.
Square roots help to simplify and solve equations where the variable is squared. It鈥檚 a powerful tool in algebra that opens the door to solving quadratic equations.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free