Posted by **Vilma** on Sunday, June 17, 2012 at 7:38pm.

I need help doing this problem, should I not get the same answer with each technique? Please help.

What three techniques can be used to solve a quadratic equation? Demonstrate these techniques on the equation:

2x² + 3x + 1 = 0

- Algebra -
**Reiny**, Sunday, June 17, 2012 at 9:00pm
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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