SOLUTION: Can someone please help? 3x^2+8x-2=0 1. Solve using Quadratic formula 2. Solve using completing the square 3. Tell which method you prefer and why

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Can someone please help? 3x^2+8x-2=0 1. Solve using Quadratic formula 2. Solve using completing the square 3. Tell which method you prefer and why      Log On


   

Question 315345: Can someone please help?
3x^2+8x-2=0
1. Solve using Quadratic formula
2. Solve using completing the square
3. Tell which method you prefer and why
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2%2B8x-2=0
1. Solve using Quadratic formula

a=3, b=8, c=-2

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ 
x+=+%28-8+%2B-+sqrt%28+8%5E2-4%2A3%2A%28-2%29+%29%29%2F%282%2A3%29+
x+=+%28-8+%2B-+sqrt%28+64%2B24+%29%29%2F6+
x+=+%28-8+%2B-+sqrt%2888+%29%29%2F6+
x+=+%28-8+%2B-+sqrt%284%2A22+%29%29%2F6+
x+=+%28-8+%2B-+2%2Asqrt%2822+%29%29%2F6+
x+=+%282%28-4+%2B-+sqrt%2822+%29%29%29%2F6+
x+=+%28-4+%2B-+sqrt%2822+%29%29%2F3+

2. Solve using completing the square

3x%5E2%2B8x-2=0

Get the constant term on the right and only x-terms on the left

3x%5E2%2B8x=2

Divide through by 3

x%5E2%2B%288%2F3%29x=2%2F3

Multiply the coefficient of x by 1%2F2:  %288%2F3%29%281%2F2%29=8%2F6=4%2F3
Square that value:  %284%2F3%29%5E2=16%2F9
Add that value to both sides:

x%5E2%2B%288%2F3%29x%2B16%2F9=2%2F3%2B16%2F9

Factor the left side: %28x%2B4%2F3%29%28x%2B4%2F3%29 or %28x%2B4%2F3%29%5E2
Combine fractions on the right side: 2%2F3%2B16%2F9=%282%2A3%29%2F%283%2A3%29%2B16%2F9=6%2F9%2B16%2F9=22%2F9

%28x%2B4%2F3%29%5E2=22%2F9

Take square roots of both sides:

x%2B4%2F3=%22%22%2B-sqrt%2822%2F9%29

x%2B4%2F3=%22%22%2B-sqrt%2822%29%2F3

Add -4%2F3 to both sides:

x=-4%2F3%2B-sqrt%2822%29%2F3

x=%28-4%2B-sqrt%2822%29%29%2F3

3. Tell which method you prefer and why

The quadratic formula because it's usually easier.

Edwin