the factor form of x square +root 2x-4
Answers
Answer:
is it an equation
Step-by-step explanation:
type question clearly
Popular Problems Algebra Solve by Factoring x- square root of 2x=4
x
−
√
2
x
=
4
Move
4
to the left side of the equation by subtracting it from both sides.
x
−
√
2
x
−
4
=
0
Move all terms not containing
√
2
x
to the right side of the equation.
Subtract
x
from both sides of the equation.
−
√
2
x
−
4
=
−
x
Add
4
to both sides of the equation.
−
√
2
x
=
−
x
+
4
Multiply each term in
−
√
2
x
=
−
x
+
4
by
−
1
Multiply each term in
−
√
2
x
=
−
x
+
4
by
−
1
.
(
−
√
2
x
)
⋅
−
1
=
(
−
x
)
⋅
−
1
+
4
⋅
−
1
Multiply
−
√
2
x
⋅
−
1
.
√
2
x
=
(
−
x
)
⋅
−
1
+
4
⋅
−
1
Simplify each term.
Multiply
(
−
x
)
⋅
−
1
.
Multiply
−
1
by
−
1
.
√
2
x
=
1
x
+
4
⋅
−
1
Multiply
x
by
1
.
√
2
x
=
x
+
4
⋅
−
1
Multiply
4
by
−
1
.
√
2
x
=
x
−
4
To remove the radical on the left side of the equation, square both sides of the equation.
√
2
x
2
=
(
x
−
4
)
2
Simplify each side of the equation.
Multiply the exponents in
(
(
2
x
)
1
2
)
2
.
Apply the power rule and multiply exponents,
(
a
m
)
n
=
a
m
n
.
(
2
x
)
1
2
⋅
2
=
(
x
−
4
)
2
Cancel the common factor of
2
.
(
2
x
)
1
=
(
x
−
4
)
2
Simplify.
2
x
=
(
x
−
4
)
2
Solve for
x
.
Simplify
(
x
−
4
)
2
.
Rewrite
(
x
−
4
)
2
as
(
x
−
4
)
(
x
−
4
)
.
2
x
=
(
x
−
4
)
(
x
−
4
)
Expand
(
x
−
4
)
(
x
−
4
)
using the FOIL Method.
2
x
=
x
⋅
x
+
x
⋅
−
4
−
4
x
−
4
⋅
−
4
Simplify and combine like terms.
2
x
=
x
2
−
8
x
+
16
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
−
8
x
+
16
=
2
x
Move all terms containing
x
to the left side of the equation.
x
2
−
10
x
+
16
=
0
Factor
x
2
−
10
x
+
16
using the AC method.
(
x
−
8
)
(
x
−
2
)
=
0
If any individual factor on the left side of the equation is equal to
0
, the entire expression will be equal to
0
.
x
−
8
=
0
x
−
2
=
0
Set the first factor equal to
0
and solve.
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x
=
8
Set the next factor equal to
0
and solve.
x
=
2
The final solution is all the values that make
(
x
−
8
)
(
x
−
2
)
=
0
true.
x
=
8
,
2
Exclude the solutions that do not make
x
−
√
2
x
−
4
=
0
true.
x
=
8