Question

Solve the quadratic with quadratic formula:

4x^2 + 10x – 1 = 0

Answer 1

`\displaystyle x=(-5 \pm √(29))/(4)`

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

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

Explanation:

Step 1: Define

4x² + 10x - 1 = 0

Step 2: Identify Variables

a = 4

b = 10

c = -1

Step 3: Find roots

1. Substitute in variables [QF]:
   `\displaystyle x=(-10\pm√(10^2-4(4)(-1)) )/(2(4))`
2. [√Radical] Exponents:
   `\displaystyle x=(-10\pm√(100-4(4)(-1)) )/(2(4))`
3. [√Radical] Multiply:
   `\displaystyle x=(-10\pm√(100+16))/(2(4))`
4. [√Radical] Add:
   `\displaystyle x=(-10\pm√(116))/(2(4))`
5. [Fraction] Multiply:
   `\displaystyle x=(-10\pm√(116))/(8)`
6. [√Radical] Simplify:
   `\displaystyle x=(-10\pm 2√(29))/(8)`
7. [Fraction] Factor:
   `\displaystyle x=(2(-5\pm √(29)))/(8)`
8. [Fraction] Simplify:
   `\displaystyle x=(-5 \pm √(29))/(4)`