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Start with the left side of the equation.
Take half of the
coefficient
to get
. In other words,
.
Now square
to get
. In other words,
Now add
and subtract
. Make sure to place this after the "s" term. Notice how
. So the expression is not changed.
Group the first three terms.
Factor
to get
.
Combine like terms.
So after completing the square,
transforms to
. So
.
So
is equivalent to
.
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Start with the completed square set to 0.
Add
to both sides.
Combine like terms.
Take the square root of both sides.
or
Break up the "plus/minus" to form two equations.
or
Take the square root of
to get
. Note:
so
or
Add
to both sides.
or
Combine the fractions
or
Combine the numerators
or
Reduce.
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Answer:
So the solutions are
or
.
