Question
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Ask by Turnbull Burgess. in the United States
Jan 30,2025

Upstudy AI Solution

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:
  1. Isolate the term with :
  2. Divide both sides by 27:
  3. 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.

Answered by UpStudy AI and reviewed by a Professional Tutor

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Simplify this solution

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!

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