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

User Betofarina
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Answer:


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)
User Ghasem Deh
by
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