Answer:
x = 7
x = 3
Explanation:
(x - 5)² - 4 = 0
Take the (x - 5)² and foil it. By doing that, you're going to set them both against each other to multiply. The squared part means that (x - 5) is being multiplied by itself. Like so:
(x - 5) (x - 5)
Multiply the x by the x, the x by the -5, the -5 by x, and the -5 by -5.
The x times x would be x². The x times -5 would be -5x. The -5 times x would be -5x. And the -5 and -5 would be 25.
To put it in an equation: x² - 5x - 5x + 25 - 4
Simply the equation: x² - 10x + 21
Now that it's a quadratic equation, we can factor. Looking at the final term, the 21, we can find factors of 21 that add up to -10, which would be -7 and -3. They both multiply to a positive 21 and add up to a -10.
Taking this new information, we can split the equation up like so: (x -7), (x - 3)
Set both equations equal to 0.
So: x - 7 = 0
Add seven to both sides.
x = 7
x - 3 = 0
Add three to both sides
x = 3
Final Answer: x = 3, x = 7, both are real solutions