Question

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

Answer 1

Answer:

$\displaystyle x=\frac{-4}{5}, \frac{-3}{5}$

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: $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$
• Multiple Roots

Step-by-step 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]:                                                $\displaystyle x=\frac{-35\pm\sqrt{35^2-4(25)(12)}}{2(25)}$
2. [Numerator - √Radical] Evaluate exponents:                                               $\displaystyle x=\frac{-35\pm\sqrt{1225-4(25)(12)}}{2(25)}$
3. [Numerator - √Radical] Multiply:                                                                   $\displaystyle x=\frac{-35\pm\sqrt{1225-1200}}{2(25)}$
4. [Numerator - √Radical] Subtract:                                                                  $\displaystyle x=\frac{-35\pm\sqrt{25}}{2(25)}$
5. [Denominator] Multiply:                                                                                  $\displaystyle x=\frac{-35\pm\sqrt{25}}{50}$
6. [Numerator - √Radical] Evaluate:                                                                  $\displaystyle x=\frac{-35\pm5}{50}$
7. Evaluate:                                                                                                         $\displaystyle x=\frac{-4}{5}, \frac{-3}{5}$