Fuentes Perkins
09/08/2023 · Middle School
Find all real solutions of the equation. \( (2 c+6)^{2}-7=0 \) \( c=\square \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Solve the equation \( (2c+6)^{2}-7=0 \).
Solve the quadratic equation by following steps:
- step0: Solve using square roots:
\(\left(2c+6\right)^{2}-7=0\)
- step1: Add or subtract both sides:
\(\left(2c+6\right)^{2}=7\)
- step2: Simplify the expression:
\(2c+6=\pm \sqrt{7}\)
- step3: Separate into possible cases:
\(\begin{align}&2c+6=\sqrt{7}\\&2c+6=-\sqrt{7}\end{align}\)
- step4: Solve the equation:
\(\begin{align}&c=\frac{\sqrt{7}-6}{2}\\&c=-\frac{\sqrt{7}+6}{2}\end{align}\)
- step5: Rewrite:
\(c_{1}=-\frac{\sqrt{7}+6}{2},c_{2}=\frac{\sqrt{7}-6}{2}\)
The real solutions of the equation \( (2c+6)^{2}-7=0 \) are \( c_{1}=-\frac{\sqrt{7}+6}{2} \) and \( c_{2}=\frac{\sqrt{7}-6}{2} \).
Quick Answer
\( c_{1}=-\frac{\sqrt{7}+6}{2} \), \( c_{2}=\frac{\sqrt{7}-6}{2} \)
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