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

Video Solution

Solution Steps

00:00 Find the largest X

00:03 First let's find X from section 1

00:08 Let's isolate X

00:13 Take the root to find X

00:23 These are the possible solutions for X from section 1

00:26 Now let's calculate X from section 2

00:32 Let's isolate X

00:41 Any number squared is always greater than 0

00:46 Minus 49 is less than 0 therefore section 2 has no solution

00:49 And this is the solution to the problem

Step-by-Step Solution

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

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.