(x-5)^2=16 square root

Question

Math Help. I don't understand what my math teacher is teaching.

Answer 1

Hi Clifford,

 

(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

 

We're finished

Answer 2

(x-5)^2=16

You have an EASY equation; on the left side, there is something squared and on the right side there is a constant number.

 

The technique for solving this type of equation is to TAKE SQUARE ROOT OF BOTH SIDES, BUT ALSO AFFIX the plus or minus symbol in front of the right side's square root.  This gives you

 

(x - 5) = ±4.  Throw away the parentheses and add 5 to both sides; this gives you x = 5 ±4.

 

So you have two answers: {1, 9}