Question

9x^2+8x-5=3x^2 to the nearest tenth

Answer 1

`x=-1.8, 0.5`

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:
  `x=(-b\pm√(b^2-4ac) )/(2a)`

Explanation:

Step 1: Define equation

9x² + 8x - 5 = 3x²

Step 2: Rewrite in Standard Form

1. Subtract 3x² on both sides: 6x² + 8x - 5 = 0

Step 3: Define variables

a = 6

b = 8

c = -5

Step 4: Find roots

1. Substitute:
   `x=(-8\pm√(8^2-4(6)(-5)) )/(2(6))`
2. Exponent:
   `x=(-8\pm√(64-4(6)(-5)) )/(2(6))`
3. Multiply:
   `x=(-8\pm√(64+120) )/(12)`
4. Add:
   `x=(-8\pm√(184) )/(12)`
5. Simplify:
   `x=(-8\pm 2√(46) )/(12)`
6. Factor GCF:
   `x=(2(-4\pm √(46)) )/(12)`
7. Divide:
   `x=(-4\pm √(46) )/(6)`
8. Evaluate:
   `x=-1.79705, 0.463722`
9. Round:
   `x=-1.8, 0.5`