Write x^2 − 6x + 7 = 0 in the form (x − a)^2 = b, where a and b are integers.

(x − 1)^2 = 4

(x − 4)^2 = 3

(x − 3)^2 = 2

(x − 2)^2 = 1

Question

Write x^2 − 6x + 7 = 0 in the form (x − a)^2 = b, where a and b are integers.

(x − 1)^2 = 4
 	
(x − 4)^2 = 3
 	
(x − 3)^2 = 2
 	
(x − 2)^2 = 1

mathstudent55 · Answer

You need to complete the square.
First, subtract 7 from both sides.
What do you get?

secretsvt · Answer

x^2 -6x=-7

thesmartone · Answer

Now

a^2 + 2ab + b^2 = (a + b)^2

So, we have to find out what the b term is so that way we can add b^2 on both sides

-6x = 2ab

We know that a = x

so

-6x = 2xb

What is b?

mathstudent55 · Answer

Good.
To complete the square, you take half of the coefficient of the x-term, and you square it.
Then you add that to both sides.
The x-term is -6x.
What is half of -6?

secretsvt · Answer

-3

mathstudent55 · Answer

Good.
Now square -3.
What do you get?

secretsvt · Answer

-9 right ?

mathstudent55 · Answer

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