Smith Bond
08/26/2024 · Senior High School
Find all real solutions to the equation: \( 5 z^{3}-80 z=5 z^{2}-80 \) \( z=\square \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Solve the equation \( 5z^{3}-80z=5z^{2}-80 \).
Solve the equation by following steps:
- step0: Solve for \(z\):
\(5z^{3}-80z=5z^{2}-80\)
- step1: Move the expression to the left side:
\(5z^{3}-80z-\left(5z^{2}-80\right)=0\)
- step2: Remove the parentheses:
\(5z^{3}-80z-5z^{2}+80=0\)
- step3: Factor the expression:
\(5\left(z-4\right)\left(z-1\right)\left(z+4\right)=0\)
- step4: Divide both sides:
\(\left(z-4\right)\left(z-1\right)\left(z+4\right)=0\)
- step5: Separate into possible cases:
\(\begin{align}&z-4=0\\&z-1=0\\&z+4=0\end{align}\)
- step6: Solve the equation:
\(\begin{align}&z=4\\&z=1\\&z=-4\end{align}\)
- step7: Rewrite:
\(z_{1}=-4,z_{2}=1,z_{3}=4\)
The real solutions to the equation \(5z^{3}-80z=5z^{2}-80\) are \(z=-4\), \(z=1\), and \(z=4\).
Quick Answer
\(z=-4\), \(z=1\), \(z=4\)
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit