Question

What are the solutions of x^2 - 2x + 10 = 0?

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Answer 1

C. x = 1 + 3i or x = 1 - 3i

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Algebra I

• Standard Form: ax² + bx + c = 0
• Quadratic Formula:
  `x=(-b\pm√(b^2-4ac) )/(2a)`

Algebra II

• Imaginary Roots: √-1 = i

Explanation:

Step 1: Define

x² - 2x + 10 = 0

Step 2: Identify Variables

a = 1

b = -2

c = 10

Step 3: Find roots

1. Substitute [Quad Formula]:
   `x=(2\pm√((-2)^2-4(1)(10)) )/(2(1))`
2. Exponents:
   `x=(2\pm√(4-4(1)(10)) )/(2(1))`
3. Multiply:
   `x=(2\pm√(4-40) )/(2)`
4. Subtract:
   `x=(2\pm√(-36) )/(2)`
5. Factor:
   `x=(2\pm√(-1) √(36) )/(2)`
6. Simplify:
   `x=(2\pm6i )/(2)`
7. Factor:
   `x=(2(1\pm3i) )/(2)`
8. Divide:
   `x=1\pm3i`