Question

What is the roots of f(x)=-x^2-6x-14

Answer 1

Answer:

$x=-3\pm i \sqrt{5}$

General Formulas and Concepts:

Pre-Algebra

• Order of Operations: BPEMDAS
• Equality Properties

Algebra I

• Standard Form: ax² + bx + c = 0
• Quadratic Formula: $x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

Algebra II

• Imaginary roots: √-1 = i

Step-by-step explanation:

Step 1: Define function

f(x) = -x² - 6x - 14

Step 2: Set up

1. Set equation equal to 0:                    -x² - 6x - 14 = 0
2. Factor out -1:                                       -(x² + 6x + 14) = 0
3. Divide both sides by -1:                      x² + 6x + 14 = 0

Step 3: Define variables

a = 1

b = 6

c = 14

Step 4: Find roots

1. Substitute:                              $x=\frac{-6\pm\sqrt{6^2-4(1)(14)} }{2(1)}$
2. Exponents:                             $x=\frac{-6\pm\sqrt{36-4(1)(14)} }{2(1)}$
3. Multiply:                                  $x=\frac{-6\pm\sqrt{36-56} }{2}$
4. Subtract:                                 $x=\frac{-6\pm\sqrt{-20} }{2}$
5. Factor:                                    $x=\frac{-6\pm\sqrt{-1} \sqrt{20} }{2}$
6. Simplify:                                  $x=\frac{-6\pm2i \sqrt{5} }{2}$
7. Factor:                                    $x=\frac{2(-3\pm i \sqrt{5} )}{2}$
8. Divide:                                    $x=-3\pm i \sqrt{5}$