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Question 742805: How to solve a linear equation for x when 3x^2 - 2x + 4 = 18 - 3x
I only get to this part which I'm guessing is wrong.
3x^2 + x = 14
See, I'm stuck. I thought all x's on one side and numbers on the other, but the answer says it's -1/3. ? Please help. The instructor only writes the couple of book examples on the board, and is no help when trying to ask a question. No clue why some people are teachers.
Thank you,
Kriss
Found 2 solutions by nerdybill, MathTherapy:
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! 3x^2 - 2x + 4 = 18 - 3x
3x^2 + x = 14 (this is ok)
However, when solving a "quadratic" (polynomial of degree 2 -- which, this is) always set one side to zero:
3x^2 + x = 14
3x^2 + x - 14 = 0
here, you factor if possible otherwise you can resort to the "quadratic formula".
.
I'll factor.
3x^2 + x - 14 = 0
to factor, you'd like to rewrite the middle term so that the coefficients add to give you 'b' (1) AND multiplies to give you ac(3*(-14)):
3x^2 + 7x - 6x - 14 = 0
notice (7-6) gives you 'b' and multiplies to give you -42
now, we group:
(3x^2 + 7x) - (6x + 14) = 0
x(3x + 7) - 2(3x + 7) = 0
(3x + 7)(x-2) = 0
x = { -7/3, 2}
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
How to solve a linear equation for x when 3x^2 - 2x + 4 = 18 - 3x
I only get to this part which I'm guessing is wrong.
3x^2 + x = 14
See, I'm stuck. I thought all x's on one side and numbers on the other, but the answer says it's -1/3. ? Please help. The instructor only writes the couple of book examples on the board, and is no help when trying to ask a question. No clue why some people are teachers.
Thank you,
Kriss
 ---- correct up to this point
Set the equation equal to zero (0), thereby getting: 
Factor the trinomial by finding two factors whose PRODUCT is c * a, or - 14 * 3, or - 42, and whose SUM is + 1. These factors are:
+ 7 and - 6
Replace the + x in the middle with + 7x - 6x, thereby resulting in: 
 ----- Grouping the polynomial on left of the equals sign
(x - 2)(3x + 7) = 0
 , or 
Don't know where you got an answer of - 1/3 from.
You can do the check!!
Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
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