Answer:
[tex]x=-0.5 \pm -i\sqrt{2}[/tex]
General Formulas and Concepts:
Pre-Algebra
- Order of Operations: BPEMDAS
Algebra I
- Standard Form: ax² + bx + c = 0
- Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
Algebra II
- Imaginary Roots: √-1 = i
- Standard Form: a + bi
Step-by-step explanation:
Step 1: Define
-4x² - 4x - 9 = 0
a = -4
b = -4
c = -9
Step 2: Find roots
- Substitute: [tex]x=\frac{4\pm\sqrt{(-4)^2-4(-4)(-9)} }{2(-4)}[/tex]
- Exponents: [tex]x=\frac{4\pm\sqrt{16-4(-4)(-9)} }{2(-4)}[/tex]
- Multiply: [tex]x=\frac{4\pm\sqrt{16-144} }{-8}[/tex]
- Subtract: [tex]x=\frac{4\pm\sqrt{-128} }{-8}[/tex]
- Factor: [tex]x=\frac{4\pm \sqrt{-1} \cdot \sqrt{128} }{-8}[/tex]
- Simplify: [tex]x=\frac{4\pm 8i\sqrt{2} }{-8}[/tex]
- Factor: [tex]x=\frac{4(1\pm 2i\sqrt{2}) }{-8}[/tex]
- Divide: [tex]x=\frac{1\pm 2i\sqrt{2}}{-2}[/tex]
- Expand: [tex]x=\frac{-1}{2} \pm \frac{-2i\sqrt{2} }{2}[/tex]
- Simplify: [tex]x=\frac{-1}{2} \pm -i\sqrt{2}[/tex]
- Evaluate: [tex]x=-0.5 \pm -i\sqrt{2}[/tex]
