Question 162302
Solve the equation
{{{(1/3)x^2}}} + {{{(1/2)x}}} = {{{1/3}}}
:
We can get rid of those annoying denominator by multiplying by 6:
6*{{{(1/3)x^2}}} + 6*{{{(1/2)x}}} = 6*{{{1/3}}}
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 = {{{1/2}}}
and
x = -2
:
Check x=-2 in original equation
{{{(1/3)(-2^2)}}} + {{{(1/2)(-2)}}} = {{{1/3}}}
{{{(1/3)(4)}}} + {{{((-2)/2)}}} = {{{1/3}}}
{{{4/3}}} - 1 = {{{1/3}}}
:
I give you the honor of checking the x = 1/2 solution