What Three Techniques Can Be Used To Solve A Quadratic Equation? Demonstrate These Techniques On The Equation X^2 - 10x - 39 = 0.

The usual techniques are
1. Factoring
x² - 10x - 39 = 0
(x-13)(x+3) = 0 (39=3*13, factors that happen to differ by the required 10)
x = 13, x = -3

2. Completing the square
x² - 10x - 39 = 0
x² - 10x + 25 = 64 (add 64 to both sides)
(x-5)² = 64 (show the square we have completed)
x-5 = ±8 (square root both sides)
x = 5±8 (add 5 to both sides)
x = {13, -3}

3. Quadratic formula (this is the same as jumping straight to the end of completing the square)
x² - 10x - 39 = 0
x = (-(-10) ±√((-10)² - 4(1)(-39)))/(2(1))
= (10 ±√(100 + 156))/2
= (10 ±√256)/2
= (10±16)/2
= 5±8
x = {13, -3}