Question

Question 5 (1 point) Solve. \[ 2 x^{2}-39=33 \] a \( \pm 3 \) b no real number solution c \( \pm 6 \) d \( d \geq \sqrt{6} \)

Ask by Hilton Ingram. in the United States
Mar 14,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The solution is \( x = \pm 6 \), so the correct answer is option (c).

Solution

Consider the equation \[ 2x^2 - 39 = 33. \] **Step 1.** Add \(39\) to both sides: \[ 2x^2 = 33 + 39 = 72. \] **Step 2.** Divide both sides by \(2\): \[ x^2 = \frac{72}{2} = 36. \] **Step 3.** Take the square root of both sides: \[ x = \pm \sqrt{36} = \pm 6. \] Thus, the solution is \( x = \pm 6 \), which corresponds to option (c).

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

Extra Insights

To solve the equation \(2x^{2}-39=33\), start by simplifying it. Add 39 to both sides to get: \[2x^{2} = 72\]. Next, divide both sides by 2 to isolate \(x^{2}\): \[x^{2} = 36\]. Now take the square root of both sides, giving you \(x = \pm 6\). So the correct answer is \(c \pm 6\). As for common mistakes, many make the error of forgetting to isolate the squared variable before taking the square root. Ensure you've simplified correctly and double-check your steps to avoid miscalculations!

Latest Algebra Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy