Solve For \[$ A \$\] In The Equation:$\[ 12 = A(8 + (-5))^2 + 3 \\]

Introduction

In this article, we will delve into solving for the variable ${ a }$ in the given equation: ${ 12 = a(8 + (-5))^2 + 3 }$. This equation involves exponentiation, addition, and multiplication, making it a complex algebraic expression. Our goal is to isolate the variable ${ a }$ and find its value.

Understanding the Equation

The given equation is: ${ 12 = a(8 + (-5))^2 + 3 }$. To begin solving for ${ a }$, we need to simplify the expression inside the parentheses. The expression ${ 8 + (-5) }$ can be evaluated as follows:

${ 8 + (-5) = 3 }$

So, the equation becomes: ${ 12 = a(3)^2 + 3 }$.

Simplifying the Equation

Now, we need to simplify the expression ${ (3)^2 }$. The exponentiation of 3 squared is equal to 9. Therefore, the equation becomes:

${ 12 = a(9) + 3 }$

Isolating the Variable ${ a }$

To isolate the variable ${ a }$, we need to get rid of the constant term 3 on the right-hand side of the equation. We can do this by subtracting 3 from both sides of the equation:

${ 12 - 3 = a(9) + 3 - 3 }$

This simplifies to:

${ 9 = a(9) }$

Solving for ${ a }$

Now, we need to isolate the variable ${ a }$ by getting rid of the coefficient 9. We can do this by dividing both sides of the equation by 9:

${ \frac{9}{9} = \frac{a(9)}{9} }$

This simplifies to:

${ 1 = a }$

Conclusion

In this article, we solved for the variable ${ a }$ in the given equation: ${ 12 = a(8 + (-5))^2 + 3 }$. By simplifying the expression inside the parentheses, we were able to isolate the variable ${ a }$ and find its value. The final solution is ${ a = 1 }$.

Step-by-Step Solution

Here is the step-by-step solution to the problem:

1. Simplify the expression inside the parentheses: ${ 8 + (-5) = 3 }$
2. Substitute the simplified expression into the original equation: ${ 12 = a(3)^2 + 3 }$
3. Simplify the expression ${ (3)^2 }$: ${ (3)^2 = 9 }$
4. Substitute the simplified expression into the equation: ${ 12 = a(9) + 3 }$
5. Subtract 3 from both sides of the equation: ${ 12 - 3 = a(9) + 3 - 3 }$
6. Simplify the equation: ${ 9 = a(9) }$
7. Divide both sides of the equation by 9: ${ \frac{9}{9} = \frac{a(9)}{9} }$
8. Simplify the equation: ${ 1 = a }$

Frequently Asked Questions

• What is the value of ${ a }$ in the equation ${ 12 = a(8 + (-5))^2 + 3 }$?
• How do you solve for ${ a }$ in the equation ${ 12 = a(8 + (-5))^2 + 3 }$?
• What is the step-by-step solution to the problem?

Final Answer

The final answer is ${ a = 1 }$.

Introduction

In our previous article, we solved for the variable ${ a }$ in the equation ${ 12 = a(8 + (-5))^2 + 3 }$. In this article, we will answer some frequently asked questions related to the problem.

Q&A

Q: What is the value of ${ a }$ in the equation ${ 12 = a(8 + (-5))^2 + 3 }$?

A: The value of ${ a }$ in the equation ${ 12 = a(8 + (-5))^2 + 3 }$ is ${ a = 1 }$.

Q: How do you solve for ${ a }$ in the equation ${ 12 = a(8 + (-5))^2 + 3 }$?

A: To solve for ${ a }$ in the equation ${ 12 = a(8 + (-5))^2 + 3 }$, you need to simplify the expression inside the parentheses, substitute the simplified expression into the original equation, and then isolate the variable ${ a }$ by getting rid of the constant term and the coefficient.

Q: What is the step-by-step solution to the problem?

A: The step-by-step solution to the problem is as follows:

1. Simplify the expression inside the parentheses: ${ 8 + (-5) = 3 }$
2. Substitute the simplified expression into the original equation: ${ 12 = a(3)^2 + 3 }$
3. Simplify the expression ${ (3)^2 }$: ${ (3)^2 = 9 }$
4. Substitute the simplified expression into the equation: ${ 12 = a(9) + 3 }$
5. Subtract 3 from both sides of the equation: ${ 12 - 3 = a(9) + 3 - 3 }$
6. Simplify the equation: ${ 9 = a(9) }$
7. Divide both sides of the equation by 9: ${ \frac{9}{9} = \frac{a(9)}{9} }$
8. Simplify the equation: ${ 1 = a }$

Q: What if the equation is more complex?

A: If the equation is more complex, you may need to use more advanced algebraic techniques, such as factoring or using the quadratic formula. However, the basic steps of simplifying the expression, isolating the variable, and solving for the variable remain the same.

Q: Can you provide more examples of solving for ${ a }$ in similar equations?

A: Yes, here are a few more examples of solving for ${ a }$ in similar equations:

• ${ 15 = a(4 + (-2))^2 + 2 }$
• ${ 20 = a(6 + (-3))^2 + 4 }$
• ${ 25 = a(8 + (-4))^2 + 5 }$

In each of these examples, you would follow the same steps as before: simplify the expression inside the parentheses, substitute the simplified expression into the original equation, and then isolate the variable ${ a }$ by getting rid of the constant term and the coefficient.

Conclusion

In this article, we answered some frequently asked questions related to solving for ${ a }$ in the equation ${ 12 = a(8 + (-5))^2 + 3 }$. We provided step-by-step solutions to the problem and discussed how to solve for ${ a }$ in similar equations.

Final Answer

The final answer is ${ a = 1 }$.