X^2-6x+9=0 solve by completing the square

x=3

Step-by-step explanation:

Step 1: Subtract 9 from both sides.

x2-6x+9-9=0-9

x2-6x=-9

Step 2: The coefficient of - 6x is - 6. Let b=-6.

Then we need to add (b/2) ^2=9 to both sides to complete the square.

Add 9 to both sides.

x2-6x+9=-9+9

x2-6x+9=0

Step 3: Factor left side.

(x-3) 2=0

Step 4: Take square root.

x-3=±√0

Step 5: Add 3 to both sides.

x-3+3=3±√0

x=3±√0

x=3+0 or x=3-0

x=3

Use the quadratic formula to find the solutions.

-

b

±

√

b

2

-

4

(

a

c

)

2

a

-

b

±

b

2

-

4

(

a

c

)

2

a

Substitute the values

a

=

1

a

=

1

,

b

=

0

b

=

0

, and

c

=

-

9

c

=

-

9

into the quadratic formula and solve for

x

x

.

0

±

√

0

2

-

4

⋅

(

1

⋅

-

9

)

2

⋅

1

0

±

0

2

-

4

⋅

(

1

⋅

-

9

)

2

⋅

1

Simplify.

Tap for more steps ...

x

=

±

3

x

=

±

3

The final answer is the combination of both solutions.

x

=

3

,

-

3