Answer:
x=5
Step-by-step explanation:
Subtract
2
from both sides of the equation.
√
2
x
−
1
=
x
−
2
To remove the radical on the left side of the equation, square both sides of the equation.
(
√
2
x
−
1
)
2
=
(
x
−
2
)
2
Simplify the left side of the equation.
2
x
−
1
=
(
x
−
2
)
2
Simplify the right side of the equation.
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2
x
−
1
=
x
2
−
4
x
+
4
Since
x
is on the right side of the equation, switch the sides so it is on the left side of the equation.
x
2
−
4
x
+
4
=
2
x
−
1
Move all terms containing
x
to the left side of the equation.
Tap for more steps...
x
2
−
6
x
+
4
=
−
1
Move
1
to the left side of the equation by adding it to both sides.
x
2
−
6
x
+
4
+
1
=
0
Add
4
and
1
.
x
2
−
6
x
+
5
=
0
Factor
x
2
−
6
x
+
5
using the AC method.
Tap for more steps...
(
x
−
5
)
(
x
−
1
)
=
0
Set
x
−
5
equal to
0
and solve for
x
.
Tap for more steps...
x
=
5
Set
x
−
1
equal to
0
and solve for
x
.
Tap for more steps...
x
=
1
The solution is the result of
x
−
5
=
0
and
x
−
1
=
0
.
x
=
5
,
1
Exclude the solutions that do not make
√
2
x
−
1
+
2
=
x
true.
x
=
5Subtract
2
from both sides of the equation.
√
2
x
−
1
=
x
−
2
To remove the radical on the left side of the equation, square both sides of the equation.
(
√
2
x
−
1
)
2
=
(
x
−
2
)
2
Simplify the left side of the equation.
2
x
−
1
=
(
x
−
2
)
2
Simplify the right side of the equation.
Tap for more steps...
2
x
−
1
=
x
2
−
4
x
+
4
Since
x
is on the right side of the equation, switch the sides so it is on the left side of the equation.
x
2
−
4
x
+
4
=
2
x
−
1
Move all terms containing
x
to the left side of the equation.
Tap for more steps...
x
2
−
6
x
+
4
=
−
1
Move
1
to the left side of the equation by adding it to both sides.
x
2
−
6
x
+
4
+
1
=
0
Add
4
and
1
.
x
2
−
6
x
+
5
=
0
Factor
x
2
−
6
x
+
5
using the AC method.
Tap for more steps...
(
x
−
5
)
(
x
−
1
)
=
0
Set
x
−
5
equal to
0
and solve for
x
.
Tap for more steps...
x
=
5
Set
x
−
1
equal to
0
and solve for
x
.
Tap for more steps...
x
=
1
The solution is the result of
x
−
5
=
0
and
x
−
1
=
0
.
x
=
5
,
1
Exclude the solutions that do not make
√
2
x
−
1
+
2
=
x
true.
x
=
5
