SOLUTION: 3q(q-2)=6

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 3q(q-2)=6      Log On


   

Question 707165: 3q(q-2)=6
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
3q%28q-2%29=6
First simplify so we can see what kind of equation we have. Using the Distributive Property to multiply we get:
3q%5E2-6q=6
This is a quadratic equation (because of the squared term). To solve it we first want one side to be zero. Subtracting 6 from each side:
3q%5E2-6q-6=0
Now we factor (or use the Quadratic Formula). We can factor out the greatest common factor of 3:
3%28q%5E2-2q-2%29=0
But now it won't factor anymore. So we must resort to the Quadratic Formula. We can use the formula on 3q%5E2-6q-6 or on q%5E2-2q-2. (The answers will be the same either way.) I'm going to use the formula on q%5E2-2q-2 because the a, b and c values are smaller.
q+=+%28-%28-2%29+%2B-+sqrt%28%28-2%29%5E2-4%281%29%28-2%29%29%29%2F2%281%29
Simplifying...
q+=+%28-%28-2%29+%2B-+sqrt%284-4%281%29%28-2%29%29%29%2F2%281%29
q+=+%28-%28-2%29+%2B-+sqrt%284%2B8%29%29%2F2%281%29
q+=+%28-%28-2%29+%2B-+sqrt%2812%29%29%2F2%281%29
q+=+%282+%2B-+sqrt%2812%29%29%2F2
q+=+%282+%2B-+sqrt%284%2A3%29%29%2F2
q+=+%282+%2B-+sqrt%284%29%2Asqrt%283%29%29%2F2
q+=+%282+%2B-+2%2Asqrt%283%29%29%2F2
q+=+%282%281+%2B-+sqrt%283%29%29%29%2F2
q+=+1+%2B-+sqrt%283%29
which is short for:
q+=+1+%2B+sqrt%283%29 or x+=+1+-+sqrt%283%29
These are the two solutions to your equation.