SOLUTION: What three techniques can be used to solve a quadratic equation? Demonstrate these techniques on the equation "12x^2 - 10x - 42 = 0".

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: What three techniques can be used to solve a quadratic equation? Demonstrate these techniques on the equation "12x^2 - 10x - 42 = 0".      Log On


   



Question 48549: What three techniques can be used to solve a quadratic equation? Demonstrate these techniques on the equation "12x^2 - 10x - 42 = 0".
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
1.)Graphing (at most times, not very accurate)
graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C12x%5E2-10x-42%2C0%29
2.)Factoring
12x%5E2+-+10x+-+42+=+0
6x%5E2+-+5x+-+21+=+0
6x%5E2+%2B+9x+-+14x+-+21+=+0
%286x%5E2+%2B+9x%29+%2B+%28-14x+-+21%29+=+0
3x%282x+%2B+3%29+-+7%282x+%2B+3%29+=+0
%283x+-+7%29%282x+%2B+3%29+=+0
3x - 7 = 0
3x = 7
x = 7/3 or 2 1/3
and
2x + 3 = 0
2x = -3
x = -3/2 or -1 1/2
3.)Completing the Square
12x%5E2+-+10x+-+42+=+0
6x%5E2+-+5x+-+21+=+0
x%5E2+-+5x%2F6+=+7%2F2
%28x+-+5%2F12%29%5E2+=+25%2F144+%2B+504%2F144+=+529%2F144
x+-+5%2F12 = +-23%2F12
x+=+5%2F12+%2B-+23%2F12
x+=+%285+%2B-+23%29%2F12
4.)Quadratic Formula
x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%285+%2B-+sqrt%28+25+%2B+504+%29%29%2F%2812%29+
x+=+%285+%2B-+23%29%2F12