Question 195350
{{{(25/2)*x^2 + 15x + 9/2 = 0}}}
Multiply both sides by {{{2}}}
{{{25x^2 + 30x + 9 = 0}}}
Use the quadratic equation
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 25}}}
{{{b = 30}}}
{{{c = 9}}}
{{{x = (-30 +- sqrt( 30^2-4*25*9 ))/(2*25) }}}
{{{x = (-30 +- sqrt( 900 - 900 )) / 50 }}}
{{{x = - 30/50}}}
{{{x = - 3/5}}}
check the answer:
{{{25/2 x² + 15x + 9/2 = 0}}}
{{{(25/2)* (-3/5)² + 15*(-3/5) + 9/2 = 0}}}
{{{9/2 - 9 + 9/2 = 0}}}
{{{9 - 18 + 9 = 0}}}
{{{0 = 0}}}
OK
I'll draw the graph of this. It touches the x-axis in 1 place,
so there is only 1 root
{{{ graph( 400, 400, -3, 1, -2, 10, (25/2)*x^2 + 15x + 9/2 ) }}}