SOLUTION: 5b. What three techniques can be used to solve a quadratic equation? Demonstrate these techniques on the equation "12x2 - 10x - 42 = 0." thank you for your help.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 5b. What three techniques can be used to solve a quadratic equation? Demonstrate these techniques on the equation "12x2 - 10x - 42 = 0." thank you for your help.      Log On


   

Question 182677: 5b.
What three techniques can be used to solve a quadratic equation? Demonstrate these techniques on the equation "12x2 - 10x - 42 = 0."
thank you for your help.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
12x%5E2-10x-42=0
1. Quadratic formula,
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-10%29+%2B-+sqrt%28+%28-10%29%5E2-4%2A12%2A%28-42%29+%29%29%2F%282%2A12%29+
x+=+%2810+%2B-+sqrt%28100%2B2016+%29%29%2F%2824%29+
x+=+%2810+%2B-+sqrt%282116+%29%29%2F%2824%29+
x+=+%2810+%2B-+46%29%2F%2824%29+
x%5B1%5D+=+%2810+%2B+46%29%2F%2824%29+
x%5B1%5D+=+%2856%29%2F%2824%29+
highlight%28x%5B1%5D+=+7%2F3%29+
x%5B2%5D+=+%2810+-+46%29%2F%2824%29+
x%5B2%5D+=+%28-36%29%2F%2824%29+
highlight%28x%5B2%5D=-%283%2F2%29%29
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2. Factor the equation,
12x%5E2-10x-42=0
%284x%2B6%29%283x-7%29=0
First solution:
4x%2B6=0
4x=-6
x=-%286%2F4%29=-%283%2F2%29
Second solution:
3x-7=0
3x=7
x=7%2F3
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3. Graph and make reasonable guesses.
+graph%28+300%2C+300%2C+-2%2C+4%2C+-2%2C+2%2C+12x%5E2-10x-42%29+
Iterate until you find the answer.
Although it's easy for this equation, it may not be the best method for every equation.