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equalizer
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Completing the Square
Choose Course
(
Algebra 1
,
Algebra 2
)
Quadratic Equations
Completing the Square
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Completing the Square 1.3 - Solution
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Return to Completing the Square
Consider the given equation.
x
2
+
1
0
x
=
-
2
0
Let's start by solving it by
completing the square
. We see above that
b
=
1
0
.
Therefore, we need to start by adding
(
2
1
0
)
2
=
2
5
to both sides.
x
2
+
1
0
x
=
-
2
0
Solve for
x
AddEqn
LHS
+
2
5
=
RHS
+
2
5
x
2
+
1
0
x
+
2
5
=
5
SplitIntoFactors
Split into factors
x
2
+
2
x
(
5
)
+
2
5
=
5
WritePow
Write as a power
x
2
+
2
x
(
5
)
+
5
2
=
5
FacPosPerfectSquare
a
2
+
2
a
b
+
b
2
=
(
a
+
b
)
2
(
x
+
5
)
2
=
5
RadicalEqn
LHS
=
RHS
x
+
5
=
±
5
SubEqn
LHS
−
5
=
RHS
−
5
x
=
-
5
±
5
We found two solutions,
x
=
-
5
+
5
and
x
=
-
5
−
5
.
Thus, we've showed that the equation can be solved by completing the square.