Question
upstudy study bank question image url

olve this equation and select the choice that ontains all of the solutions. \[ x^{2}-2 x+2=0 \]

Ask by Cervantes Barber. in the United States
Mar 14,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The solutions are \( x = 1 + i \) and \( x = 1 - i \).

Solution

We are given the quadratic equation: \[ x^2 - 2x + 2 = 0 \] **Step 1.** Identify the coefficients from the standard form \( ax^2 + bx + c = 0 \): \[ a = 1,\quad b = -2,\quad c = 2 \] **Step 2.** Use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Substitute the values: \[ x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(2)}}{2(1)} = \frac{2 \pm \sqrt{4 - 8}}{2} \] **Step 3.** Simplify under the square root: \[ \sqrt{4 - 8} = \sqrt{-4} = 2i \] **Step 4.** Write the solutions: \[ x = \frac{2 \pm 2i}{2} = 1 \pm i \] Thus, the two solutions to the equation are: \[ x = 1+i \quad \text{and} \quad x = 1-i \]

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

The Deep Dive

To solve the equation \( x^{2}-2x+2=0 \), we can use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Here, \( a = 1 \), \( b = -2 \), and \( c = 2 \). Plugging in these values gives: \[ x = \frac{2 \pm \sqrt{(-2)^2 - 4 \cdot 1 \cdot 2}}{2 \cdot 1} = \frac{2 \pm \sqrt{4 - 8}}{2} = \frac{2 \pm \sqrt{-4}}{2} = \frac{2 \pm 2i}{2} = 1 \pm i \] Thus, the solutions are \( x = 1 + i \) and \( x = 1 - i \). The choice that contains all the solutions is: \( \{1 + i, 1 - i\} \). Remember, when you’re dealing with complex numbers, they always come in pairs of conjugates when derived from real coefficients!

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