Question
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Tutor-Verified Answer
Answer
Solution
Solve the equation by following steps:
- step0: Solve for
:
- step1: Move the constant to the right side:
- step2: Remove 0:
- step3: Divide both sides:
- step4: Divide the numbers:
- step5: Simplify the equation:
- step6: Calculate:
- step7: Simplify the root:
To solve the equation, we can follow these steps:
-
Isolate the term with
: -
Divide both sides by 27:
-
Take the cube root of both sides:
Thus, the solution to the equation
is:
Alternatively, this can also be expressed as:
Both forms represent the same value.
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Extra Insights
To solve the equation
, we can factor it using the difference of cubes formula,
. Here, we have
and
. Thus, we rewrite the equation as:
Factoring it gives us:
This breaks down to:
Setting each factor to zero, we first solve
, leading to
. The other factor,
, can be solved using the quadratic formula
. Substituting
:
So, the complete solutions for the equation
are:
Now, that’s a sweet mix of real and complex numbers!