Solve the Quadratic Equations: x² + 9 = 0 and 2x² + 8 = 0 Compared

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

• Step 1: Solve the equation $x^2 + 9 = 0$
• Step 2: Solve the equation $2x^2 + 8 = 0$
• Step 3: Compare the solutions (if any) to identify the largest $x$

Step 1: Solving $x^2 + 9 = 0$:
First, isolate $x^2$ by subtracting $9$ from both sides:
$x^2 = -9$.
Since $x^2 = -9$, trying to find the square root leads to $x = \pm \sqrt{-9}$,
which involves the imaginary unit $i$, hence no real solution exists.

Step 2: Solving $2x^2 + 8 = 0$:
First, isolate $2x^2$ by subtracting $8$ from both sides:
$2x^2 = -8$.
Divide each side by $2$:
$x^2 = -4$.
Attempting to take the square root results in $x = \pm \sqrt{-4}$,
which similarly involves the imaginary unit $i$, so no real solution exists.

Step 3: Compare the solutions:
Since both equations yield no real solutions, there is no value of $x$ to compare.

Therefore, there is no solution to the two equations.