Question

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

Answer 1

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.
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x
=
±
3
x
=
±
3
The final answer is the combination of both solutions.
x
=
3
,
−
3

Answer 2

Answer:

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