# How do you solve #(x - 1)^2 = 9#?

##### 2 Answers

x1= 4 and x2=-2

#### Explanation:

x^2 - 2x*1 +1^2 = 9

x^2-2x+1=9

since this is a quadratic equation it has to be equal to 0, so:

x^2-2x+1-9=0

x^2-2x-8=0

we can solve this in two ways: the first way is to find the factors of x^2-2x-8 and the second one is to solve it by using the quadratic formula.

Let me factorize it.

(x-4)(x+2)=0

In order for this to be equal zero:

x-4=0 => x=4

and

x+2=0 => x=-2

The quadratic equation has always two roots or two solutions. Consequently, x1= 4 and x2=-2.

#### Explanation:

#color(blue)((x-1)^2=9#

Use the golden rule of Algebra: What you do on one side must be done on the other side also

Take the square root of both sides (

Use:

But,

Solve for both

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Add

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Add

#color(blue)( ul bar |x=(4,-2)|#