```Question 77053
Solve 1/3x2-1/2x=1/6. The 2 beside the 1/3x is supposed to represent squared.
:
(1/3)x^2 - (1/2)x = 1/6
:
Get rid of those denominators, multiply equation by 6 and you have:
2x^2 - 3x = 1
:
2x^2 - 3x - 1 = 0; subtracted 1 from both sides, a quadratic equation
:
Use the quadratic formula to find x; a=2; b=-3; c = -1
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
:
{{{x = (-(-3) +- sqrt( (-3)^2 - 4 * 2 * -1 ))/(2*2) }}}
:
{{{x = (+3 +- sqrt( 9 - (-8) ))/(4) }}}
:
{{{x = (+3 +- sqrt( 9 + 8 ))/(4) }}}
:
{{{x = (+3 +- sqrt(17))/(4) }}}
:
{{{x = (+3 +- sqrt( 9 - (-8) ))/(4) }}}
:
{{{x = (+3 +- sqrt( 9 + 8))/(4) }}}
:
{{{x = (+3 +- sqrt(17))/(4) }}}
:
{{{x = (+3 + 4.123)/(4) }}}: 1st solution
:
{{{x = 7.123/4}}}
x = +1.78
:
{{{x = (+3 -4.123)/(4) }}}: 2nd solution
:
{{{x = (-1.123)/(4) }}}
x = -.28
:
Check x = 1.78 in the original equation:
(1/3)1.78^2 - (1/2)1.78 = 1/6
(1/3)3.17 - (1/2)1.78 = 1/6
1.056 - .89 = .166 which is about 1/6
:
I'll let you check the x = -.28 solution```