Question

Solve the equation by taking square roots

(x-3)^2 +8 = -10​

Answer 1

x = 3 ± 3i√2

General Formulas and Concepts:

Pre-Algebra

• Order of Operations: BPEMDAS
• Equality Properties

Algebra I

• Vertex Form: f(x) = a(bx - c)ⁿ + d
• Completing the Square
• Solving roots

Algebra II

• Imaginary Roots: √-1 = i

Explanation:

Step 1: Define equation

(x - 3)² + 8 = -10

Step 2: Solve for x

1. Subtract 8 on both sides: (x - 3)² = -18
2. Square root both sides: x - 3 = ±√-18
3. Factor: x - 3 = √-1 · ±√18
4. Simplify: x - 3 = ±3i√2
5. Add 3 to both sides: x = 3 ± 3i√2