SOLUTION: 3x^2 +3x =21. Solve this problem by using the quadratic formula. Show all work. Thank you.

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Question 1063605: 3x^2 +3x =21. Solve this problem by using the quadratic formula. Show all work.
Thank you.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
ax%5E2%2Bbx%2Bc=0 has the solutions x=%28-b%2B-+sqrt%28b%5E2-4ac%29%29%2F%282a%29.

3x%5E2+%2B3x+=21
3x%5E2%2B3x-21=0
x%5E2%2Bx-7=0

x=%28-1%2B-+sqrt%281%5E2-4%2A1%2A%28-7%29%29%29%2F2

x=%28-1%2B-+sqrt%281%2B28%29%29%2F2

x=%28-1%2B-+sqrt%2829%29%29%2F2

system%28x=-1%2F2-sqrt%2829%29%2F2%2COR%2Cx=-1%2F2%2Bsqrt%2829%29%2F2%29

Answer by ikleyn(52795) About Me  (Show Source):
You can put this solution on YOUR website!
.
3x^2 +3x =21. Solve this problem by using the quadratic formula. Show all work.
Thank you.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

3x%5E2+%2B3x = 21     Divide both sides by 3

x%5E2+%2B+x = 7  --->

x%5E2+%2B+x+-+7 = 0.

Apply the quadratic formula

    (for the general quadratic equation ax%5E2+%2B+bx+%2B+c = 0 it is x%5B1%2C2%5D = %28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F%282a%29 ).

So, in your case you have 

    x%5B1%2C2%5D = %28-1+%2B-+sqrt%28%28-1%29%5E2+-+4%2A1%2A%28-7%29%29%29%2F%282%2A1%29 = %28-1+%2B-+sqrt%2829%29%29%2F2.

Answer.  x%5B1%5D = %28-1+%2B+sqrt%2829%29%29%2F2,   x%5B2%5D = %28-1+%2B+sqrt%2829%29%29%2F2.

Now listen to me very attentively.

The quadratic formula is described everywhere, in every and each algebra textbook.

You can read about it in the lessons
    - Introduction into Quadratic Equations
    - PROOF of quadratic formula by completing the square
in this site.

So, applying this formula and making these calculations is absolutely mechanical work.

We, tutors, usually do not do such work for students, assuming that it is students' work, not the tutors' work.

As you ask us to do it, I presume you are for the first time applying the quadratic formula.
It is the only reason why I did it for you.

For the future, memorize: IT IS YOUR JOB.