Answer:
[tex]x=-3\pm i \sqrt{5}[/tex]
General Formulas and Concepts:
Pre-Algebra
- Order of Operations: BPEMDAS
- Equality Properties
Algebra I
- Standard Form: ax² + bx + c = 0
- Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
Algebra II
Step-by-step explanation:
Step 1: Define function
f(x) = -x² - 6x - 14
Step 2: Set up
- Set equation equal to 0: -x² - 6x - 14 = 0
- Factor out -1: -(x² + 6x + 14) = 0
- Divide both sides by -1: x² + 6x + 14 = 0
Step 3: Define variables
a = 1
b = 6
c = 14
Step 4: Find roots
- Substitute: [tex]x=\frac{-6\pm\sqrt{6^2-4(1)(14)} }{2(1)}[/tex]
- Exponents: [tex]x=\frac{-6\pm\sqrt{36-4(1)(14)} }{2(1)}[/tex]
- Multiply: [tex]x=\frac{-6\pm\sqrt{36-56} }{2}[/tex]
- Subtract: [tex]x=\frac{-6\pm\sqrt{-20} }{2}[/tex]
- Factor: [tex]x=\frac{-6\pm\sqrt{-1} \sqrt{20} }{2}[/tex]
- Simplify: [tex]x=\frac{-6\pm2i \sqrt{5} }{2}[/tex]
- Factor: [tex]x=\frac{2(-3\pm i \sqrt{5} )}{2}[/tex]
- Divide: [tex]x=-3\pm i \sqrt{5}[/tex]
