Question

Solve 2x2 + 4x = 30 using the Quadratic Formula.

Answer 1

`x=-5, 3`

General Formulas and Concepts:

Pre-Algebra

• Order of Operations: BPEMDAS

Algebra I

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

Explanation:

Step 1: Define equation

2x² + 4x = 30

Step 2: Rewrite into Standard Form

2x² + 4x - 30 = 0

Step 3: Define variables

a = 2

b = 4

c = -30

Step 4: Solve for x

1. Substitute:
   `x=(-4\pm√(4^2-4(2)(-30)) )/(2(2))`
2. Evaluate:
   `x=(-4\pm√(16-4(2)(-30)) )/(2(2))`
3. Multiply:
   `x=\frac{-4\pm√(16+240) }4}`
4. Add:
   `x=\frac{-4\pm√(256) }4}`
5. Evaluate:
   `x=\frac{-4\pm16 }4}`
6. Factor:
   `x=\frac{4(-1\pm4)}4}`
7. Divide:
   `x=(-1\pm4)`
8. Add/Subtract:
   `x=-5, 3`

And we have our final answer!