Hi okay i’m gonna write the explanation i hope you give me a brilliant if you think I’m deserving it thank you
(x-5)2=16
The first step you can take to solve this quadratic is to take the square root of both sides of the equation.
√[(x-5)2]=√(16)
When you take the square root of a term that is square it equals what is inside the parentheses.
So on the left side, you have x-5
On the right side, you are what we call "forcing" the square root. When this happens, you need to put ±. Why? Good question. When you square a negative number it positive; when you square a positive number it is also positive.
The √16 = ±4
So now we have;
x-5=±4
What do you do with that?
You make two separate equations.
x-5=4 and x-5=-4
x=9 x=1
Let's check our answers
x=9
(x-5)2=16
(9-5)2=16
42=16
16=16 it checks
x=1
(x-5)2=16
(1-5)2=16
(-4)2=16
16=16 it also checks
ANSWER: x=9 and x=1
