Solve the Equation x² + 8² = 3x² + 16

Solve the exercise:

$x^2+8^2=3x^2+16$

To solve this equation, we'll follow these steps:

• Step 1: Understand and restate the problem.
• Step 2: Rearrange the equation to group terms effectively.
• Step 3: Solve for $x$.

Now, let's work through each step:

Step 1: We begin with the equation $x^2 + 8^2 = 3x^2 + 16$. Our objective is to find the value(s) of $x$ that satisfy this equation. The equation is already composed of square terms and constants, providing a clue to equate similar terms and solve for $x$.

Step 2: Let's rearrange the given equation:
\begin{align*} x^2 + 64 &= 3x^2 + 16 \end{align*}

Subtract $x^2$ from both sides:
\begin{align*} 64 &= 3x^2 - x^2 + 16 \end{align*}

Which simplifies to:
\begin{align*} 64 &= 2x^2 + 16 \end{align*}

Next, subtract 16 from both sides:
\begin{align*} 64 - 16 &= 2x^2 \\ 48 &= 2x^2 \end{align*}

Now, divide both sides by 2 to further isolate $x^2$:
\begin{align*} 24 &= x^2 \end{align*}

Step 3: Solve for $x$ by taking the square root of both sides. Remember to consider both the positive and negative roots because squaring a number always yields a positive result:
\begin{align*} x &= \pm \sqrt{24} \end{align*}

Conclusion: The solutions to the equation are $x = \pm \sqrt{24}$.

Therefore, the correct answer choice is: $\pm \sqrt{24}$.