Question 428519
{{{ x^2 = 3x + 10 }}}
Subtract {{{ 3x + 10 }}}
from both sides
{{{x^2 - 3x - 10 = 0 }}}
The equation now has the form
{{{ax^2 + b*x + c = 0}}}
Solve using the quadratic equation
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 1}}}
{{{b = -3}}}
{{{c = -10}}}
{{{x = (-(-3) +- sqrt( (-3)^2-4*1*(-10) ))/(2*1) }}}
{{{x = ( 3 +- sqrt( 9 + 40 )) / 2 }}}
{{{x = ( 3 +- 7) / 2 }}}
{{{ x = 5 }}}
and
{{{ x = -2 }}}
------------
You can check just by rewriting these results:
{{{ x = 5 }}}
{{{x - 5 = 0 }}}
and
{{{x = -2 }}}
{{{ x + 2 = 0 }}}
Now you can say
{{{ (x - 5)*(x + 2) = 0 }}}
{{{ x^2 - 3x - 10 = 0 }}}
OK