Question

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

Answer 1

Answer:

$x=-0.5 \pm -i\sqrt{2}$

General Formulas and Concepts:

Pre-Algebra

• Order of Operations: BPEMDAS

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
• 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

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