# Algebra

What three techniques can be used to solve a quadratic equation? Demonstrate these techniques on the equation:
2x² + 3x + 1 = 0

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1. 1. Factoring (works only in special cases)
(2x+1)(x+1) = 0
2x+1=0 or x+1=0
x = -1/2 or x = -1

2. completing the square, works all the time
(I use this method when the coefficient of the square term is 1 and the middle term is even)

divide by 2
x^2 + (3/2)x = -1/2
take 1/2 the coefficient of the middle term, square it and add it to both sides
x^2 + (3/2)x + 9/16 = -1/2 + 9/16
(x+ 3/4)^2 = 1/16
take √ of both sides
x+3/4 = ± 1/4
x = -3/4 ± 1/4
x = -1/2 or x = -1

3. The quadratic formula, works all the time.
x = (-3 ± √(9-4(2)(1))/4
= (-3 ±√1)/4
= -1/2 or -1

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