SOLUTION: Solve the equation 1/3 x^2 + 1/2x = 1/3

Question 162302: Solve the equation
1/3 x^2 + 1/2x = 1/3
Found 2 solutions by ankor@dixie-net.com, Alan3354:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Solve the equation
+ =
:
We can get rid of those annoying denominator by multiplying by 6:
6* + 6* = 6*
Cancel out the denominators and you have:
2x^2 + 3x = 2
:
Arrange as a quadratic equation:
2x^2 + 3x - 2 = 0
:
This factors to:
(2x - 1)(x + 2) = 0
:
2x = +1
x =
and
x = -2
:
Check x=-2 in original equation
+ =
+ =
- 1 =
:
I give you the honor of checking the x = 1/2 solution
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Solve the equation
1/3 x^2 + 1/2x = 1/3
---------------
Multiply by 6
2x^2 + 3x = 2
2x^2 + 3x - 2 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=25 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.5, -2. Here's your graph:

The onsite solver gets the right answers, but the factors are not right when the coefficient of the x^2 term is not 1.

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