Solve x²-49=0 vs x²+49=0: Finding the Largest X-Value

Solve each equation separately and find which x is the largest.

1. $x^2-49=0$

2. $x^2+49=0$

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

• Step 1: Solve the first equation $x^2 - 49 = 0$.
• Step 2: Solve the second equation $x^2 + 49 = 0$.
• Step 3: Compare the $x$ values to determine which is largest.

Now, let's work through each step:

Step 1: Solve $x^2 - 49 = 0$.

Add 49 to both sides to isolate the square term: $x^2 = 49$.

Take the square root of both sides to find $x$:
$x = \pm \sqrt{49}$
$x = \pm 7$.

So, the solutions are $x = 7$ and $x = -7$.

Step 2: Solve $x^2 + 49 = 0$.

Subtract 49 from both sides to isolate the square term: $x^2 = -49$.

Take the square root of both sides considering complex numbers:
$x = \pm \sqrt{-49}$
Using imaginary numbers: $x = \pm 7i$.

These solutions are non-real complex numbers.

Step 3: Compare the solutions.

For the first equation, the real solutions are $x = 7$ and $x = -7$.

Since the second equation only has imaginary solutions, the largest real $x$ is from the first equation: $x = 7$.

Therefore, the largest $x$ is 7.