Tid Bits from Chapter 2

Deriving the Quadratic Formula: 
Solve ax² + bx + c = 0 by completing the square as follows:
1. Subtract c from both sides
ax² + bx = -c
2. Divide both sides by a, the leading coefficient

x² + b/a x = -c/a

3. Add the square of half of b/a, that is, (b/2a)², to both sides

x² + b/a x + (b/2a)²= -c/a (b/2a)²

4. Write the left side of the equation as a perfect square

(x + b/2a)² = (b/2a)²-c/a

5. Take the square root of both sides

x + b/2a = √(b/2a)²-c/a

6. Subtract b/2a from both sides

x = -b/2a + or - √(b²-4ac)/(2a)

Quadratic Formula:

x = -b/2a + or - √(b²-4ac)/(2a)