SOLUTION: Solve using completing the square method the equation: 3x^2 + 11x + 4 = 0

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Question 896456: Solve using completing the square method the equation: 3x^2 + 11x + 4 = 0
Found 2 solutions by thesvw, MathTherapy:
Answer by thesvw(77) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2+%2B+11x+%2B+4+=0
Get 3 as a factor ..
3%28x%5E2+%2B+11x%2F3+%2B+4%2F3%29+=+0
Divide 11/3 by 2 and square it. And subtract it. So nothing changes. Hope you understand.
3%28x%5E2+%2B+11x%2F3+%2B+%2811%2F6%29%5E2+%2B+4%2F3+-+%2811%2F6%29%5E2+%29
Now you know .. you can complete square like this..
3%28%28x%2B+11%2F6%29%5E2+%2B+4%2F3+-+%2811%2F6%29%5E2%29
%2811%2F6%29%5E2+=+121%2F36
4%2F3+-+121%2F36
%2848-121%29%2F36
%28-73%2F36%29
3%28%28x%2B11%2F6%29%5E2+-+%2873%2F36%29%29
3%2A%28x+%2B+11%2F6%29%5E2+-+73%2F12
There you got the answer.
I will tell you an easy way to remember square completing
Just divide the coefficient with x and put it in with the original x. Now subtract the remaining number with no variable by the square of the number inside the bracket which you have made a while ago.
Ex :- x%5E2+%2B+4x+%2B+8
Divide 4 by 2 and put inside.
%28x+%2B+2%29%5E2 . Done.. now you have 8 remaining.
%28x+%2B2%29%5E2+%2B8+-+4
%28x%2B2%29%5E2+%2B+4

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Solve using completing the square method the equation: 3x^2 + 11x + 4 = 0

3x%5E2+%2B+11x+%2B+4+=+0
3x%5E2+%2B+11x+=+-+4
3x%5E2%2F3+%2B+11x%2F3+=+%28-+4%29%2F3 ----- Dividing by GCF, 3 to make leading coefficient (x%5E2), 1
x%5E2+%2B+%2811%2F3%29x+=+-+4%2F3
x%5E2+%2B+%2811%2F3%29x+%2B+____+=+-+4%2F3+%2B+____
x%5E2+%2B+%2811%2F3%29x+%2B+%2811%2F6%29%5E2+=+-+4%2F3+%2B+%2811%2F6%29%5E2 ----- Halving b, or (11%2F3), squaring it, and then adding to both sides
%28x+%2B+11%2F6%29%5E2+=+-+4%2F3+%2B+%2811%2F6%29%5E2
%28x+%2B+11%2F6%29%5E2+=+-+4%2F3+%2B+121%2F36
%28x+%2B+11%2F6%29%5E2+=+-+48%2F36+%2B+121%2F36
%28x+%2B+11%2F6%29%5E2+=+73%2F36
x+%2B+11%2F6+=+0+%2B-+sqrt%2873%2F36%29 -------- Taking square root of both sides
x+=+-+11%2F6+%2B-+sqrt%2873%2F36%29+%96+11%2F6
x+=+-+11%2F6+%2B+sqrt%2873%29%2F6 OR x+=+-+11%2F6+-+%28sqrt%2873%29%29%2F6
highlight_green%28x+=+%28sqrt%2873%29+-+11%29%2F6%29 OR highlight_green%28x+=+%28-+sqrt%2873%29+-+11%29%2F6%29