Question

Solve equation by using the quadratic formula 25x^2 + 35x = -12​

Answer 1

`\displaystyle x=(-4)/(5), (-3)/(5)`

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

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtract Property of Equality

Algebra I

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

Explanation:

Step 1: Define

25x² + 35x = -12

Step 2: Rewrite

1. [Addition Property of Equality] Add 12 on both sides: 25x² + 35x + 12 = 0

Step 3: Identify

Identify Variable Parts.

a = 25, b = 35, c = 12

Step 4: Solve for x

1. Substitute in variables [Quadratic Formula]:
   `\displaystyle x=(-35\pm√(35^2-4(25)(12)))/(2(25))`
2. [Numerator - √Radical] Evaluate exponents:
   `\displaystyle x=(-35\pm√(1225-4(25)(12)))/(2(25))`
3. [Numerator - √Radical] Multiply:
   `\displaystyle x=(-35\pm√(1225-1200))/(2(25))`
4. [Numerator - √Radical] Subtract:
   `\displaystyle x=(-35\pm√(25))/(2(25))`
5. [Denominator] Multiply:
   `\displaystyle x=(-35\pm√(25))/(50)`
6. [Numerator - √Radical] Evaluate:
   `\displaystyle x=(-35\pm5)/(50)`
7. Evaluate:
   `\displaystyle x=(-4)/(5), (-3)/(5)`