Question

Use the quadratic formula to solve for x. 3x2 = 8x-1 Round your answer to the nearest hundredth. If there is more than one solution, separate them with commas. = 0 X $ ?​

Answer 1

`x \approx 0.13, 2.54`

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Algebra I

• Standard Form: ax² + bx + c = 0
• Quadratic Formula:
  `x=(-b\pm√(b^2-4ac) )/(2a)`

Explanation:

Step 1: Define

3x² = 8x - 1

Step 2: Rewrite

Put equation in Standard Form

1. Subtract 8x on both sides: 3x² - 8x = -1
2. Add 1 to both sides: 3x² - 8x + 1 = 0

Step 3: Identify Variables

a = 3

b = -8

c = 1

Step 4: Solve for x

1. Substitute [Quad Formula]:
   `x=(8\pm√((-8)^2-4(3)(1)) )/(2(3))`
2. Evaluate Exponents:
   `x=(8\pm√(64-4(3)(1)) )/(2(3))`
3. Multiplication:
   `x=(8\pm√(64-12) )/(6)`
4. Subtraction:
   `x=(8\pm√(52) )/(6)`
5. Simplify Radical:
   `x=(8\pm2√(13) )/(6)`
6. Factor GCF:
   `x=(2(4\pm√(13)) )/(6)`
7. Simplify Fraction:
   `x=(4\pm√(13))/(3)`
8. Evaluate:
   `x=0.131483, 2.53518`
9. Round:
   `x \approx 0.13, 2.54`