Answer:
[tex]x=-1.8, 0.5[/tex]
General Formulas and Concepts:
Pre-Algebra
- Order of Operations: BPEMDAS
- Equality Properties
Algebra I
- Combining Like Terms
- Standard Form: ax² + bx + c = 0
- Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
Step-by-step explanation:
Step 1: Define equation
9x² + 8x - 5 = 3x²
Step 2: Rewrite in Standard Form
- Subtract 3x² on both sides: 6x² + 8x - 5 = 0
Step 3: Define variables
a = 6
b = 8
c = -5
Step 4: Find roots
- Substitute: [tex]x=\frac{-8\pm\sqrt{8^2-4(6)(-5)} }{2(6)}[/tex]
- Exponent: [tex]x=\frac{-8\pm\sqrt{64-4(6)(-5)} }{2(6)}[/tex]
- Multiply: [tex]x=\frac{-8\pm\sqrt{64+120} }{12}[/tex]
- Add: [tex]x=\frac{-8\pm\sqrt{184} }{12}[/tex]
- Simplify: [tex]x=\frac{-8\pm 2\sqrt{46} }{12}[/tex]
- Factor GCF: [tex]x=\frac{2(-4\pm \sqrt{46}) }{12}[/tex]
- Divide: [tex]x=\frac{-4\pm \sqrt{46} }{6}[/tex]
- Evaluate: [tex]x=-1.79705, 0.463722[/tex]
- Round: [tex]x=-1.8, 0.5[/tex]
