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Answer
The solutions are
and
.
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The Deep Dive
To solve the equation
, first square both sides to eliminate the square root:
Now expand the right side:
Next, rearrange the equation to set it to zero:
This simplifies to:
Now, use the quadratic formula
, where
,
, and
:
Now, remember to check for extraneous solutions since we squared the equation. Substituting
back into the original equation confirms it works. However,
should also be checked, but since
is more than 2, this value results in a negative square root, and thus doesn’t satisfy the original equation.
Final answer: