Question

Solve - 4x2 - 4x - 9 = 0, stating your solutions in the form a = bi. Someone please answer!!

Answer 1

`x=-0.5 \pm -i√(2)`

General Formulas and Concepts:

Pre-Algebra

• Order of Operations: BPEMDAS

Algebra I

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

Algebra II

• Imaginary Roots: √-1 = i
• Standard Form: a + bi

Explanation:

Step 1: Define

-4x² - 4x - 9 = 0

a = -4

b = -4

c = -9

Step 2: Find roots

1. Substitute:
   `x=(4\pm√((-4)^2-4(-4)(-9)) )/(2(-4))`
2. Exponents:
   `x=(4\pm√(16-4(-4)(-9)) )/(2(-4))`
3. Multiply:
   `x=(4\pm√(16-144) )/(-8)`
4. Subtract:
   `x=(4\pm√(-128) )/(-8)`
5. Factor:
   `x=(4\pm √(-1) \cdot √(128) )/(-8)`
6. Simplify:
   `x=(4\pm 8i√(2) )/(-8)`
7. Factor:
   `x=(4(1\pm 2i√(2)) )/(-8)`
8. Divide:
   `x=(1\pm 2i√(2))/(-2)`
9. Expand:
   `x=(-1)/(2) \pm (-2i√(2) )/(2)`
10. Simplify:
    `x=(-1)/(2) \pm -i√(2)`
11. Evaluate:
    `x=-0.5 \pm -i√(2)`