7(t+12)^6-20=323 What Is X

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Introduction

In this article, we will be solving a complex equation involving exponents and variables. The equation given is 7(t+12)^6-20=323, and we need to find the value of 't'. This equation requires a step-by-step approach to simplify and solve for the variable 't'.

Understanding the Equation

The given equation is 7(t+12)^6-20=323. To solve for 't', we need to isolate the variable 't' on one side of the equation. The equation involves an exponent of 6, which means we will need to use the properties of exponents to simplify the equation.

Step 1: Simplify the Equation

The first step is to simplify the equation by isolating the term with the exponent. We can start by adding 20 to both sides of the equation to get rid of the -20 on the left side.

7(t+12)^6-20+20=323+20

This simplifies to:

7(t+12)^6=343

Step 2: Divide by 7

Next, we need to get rid of the coefficient 7 by dividing both sides of the equation by 7.

\frac{7(t+12)^6}{7}=\frac{343}{7}

This simplifies to:

(t+12)^6=49

Step 3: Take the 6th Root

To get rid of the exponent 6, we need to take the 6th root of both sides of the equation.

\sqrt[6]{(t+12)^6}=\sqrt[6]{49}

This simplifies to:

t+12=7

Step 4: Solve for 't'

Finally, we can solve for 't' by subtracting 12 from both sides of the equation.

t+12-12=7-12

This simplifies to:

t=-5

Conclusion

In this article, we solved the equation 7(t+12)^6-20=323 to find the value of 't'. We used the properties of exponents to simplify the equation and isolate the variable 't'. The final answer is t=-5.

Tips and Tricks

  • When solving equations with exponents, it's essential to use the properties of exponents to simplify the equation.
  • Make sure to isolate the variable on one side of the equation to solve for it.
  • Use the order of operations (PEMDAS) to simplify the equation.

Common Mistakes

  • Not using the properties of exponents to simplify the equation.
  • Not isolating the variable on one side of the equation.
  • Not following the order of operations (PEMDAS).

Real-World Applications

Solving equations with exponents has many real-world applications, such as:

  • Physics: To calculate the energy of a particle or the frequency of a wave.
  • Engineering: To design and optimize systems, such as bridges or buildings.
  • Computer Science: To solve complex problems in algorithms and data structures.

Final Thoughts

Introduction

In our previous article, we solved the equation 7(t+12)^6-20=323 to find the value of 't'. In this article, we will answer some frequently asked questions related to solving this equation.

Q: What is the first step in solving the equation 7(t+12)^6-20=323?

A: The first step in solving the equation 7(t+12)^6-20=323 is to simplify the equation by isolating the term with the exponent. We can start by adding 20 to both sides of the equation to get rid of the -20 on the left side.

Q: Why do we need to use the properties of exponents to simplify the equation?

A: We need to use the properties of exponents to simplify the equation because the equation involves an exponent of 6. By using the properties of exponents, we can simplify the equation and make it easier to solve for the variable 't'.

Q: What is the order of operations (PEMDAS) and how does it apply to solving this equation?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

  • Parentheses: Evaluate expressions inside parentheses first.
  • Exponents: Evaluate any exponential expressions next.
  • Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  • Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

In the equation 7(t+12)^6-20=323, we need to follow the order of operations to simplify the equation.

Q: What is the final answer to the equation 7(t+12)^6-20=323?

A: The final answer to the equation 7(t+12)^6-20=323 is t=-5.

Q: How does solving this equation apply to real-world problems?

A: Solving the equation 7(t+12)^6-20=323 has many real-world applications, such as:

  • Physics: To calculate the energy of a particle or the frequency of a wave.
  • Engineering: To design and optimize systems, such as bridges or buildings.
  • Computer Science: To solve complex problems in algorithms and data structures.

Q: What are some common mistakes to avoid when solving this equation?

A: Some common mistakes to avoid when solving the equation 7(t+12)^6-20=323 include:

  • Not using the properties of exponents to simplify the equation.
  • Not isolating the variable on one side of the equation.
  • Not following the order of operations (PEMDAS).

Q: How can I practice solving equations like this one?

A: You can practice solving equations like this one by:

  • Working through example problems in your textbook or online resources.
  • Creating your own practice problems and solving them.
  • Joining a study group or working with a tutor to get help and feedback.

Conclusion

In this article, we answered some frequently asked questions related to solving the equation 7(t+12)^6-20=323. We covered topics such as the first step in solving the equation, the importance of using the properties of exponents, and the order of operations (PEMDAS). We also discussed the final answer to the equation and its real-world applications. By following the steps outlined in this article, you can solve for the value of 't' and apply the concepts to real-world problems.