Question 171916
First add {{{1}}} to both sides
{{{3x^2 + 5x = 1}}}
Now divide both sides by {{{3}}}
{{{x^2 + (5/3)*x = 1/3}}}
Take 1/2 of the coefficient of {{{x}}}, square it
and add it to both sides
{{{x^2 + (5/3)*x + (5/6)^2 = (5/6)^2 + 1/3}}}
The thing to realize at this point is that the
left side is a perfect square. It is
{{{(x + 5/6)^2}}}, so
{{{(x + 5/6)^2 = 25/36 + 12/36}}}
{{{(x + 5/6)^2 = 37/36}}}
Take the square root of both sides
{{{x + 5/6 = sqrt(37)/6}}}
Solve for {{{x}}}
{{{x = (sqrt(37) - 5) / 6}}}
and
{{{x = (-sqrt(37) - 5) / 6}}}
Both answers are correct