Question 1068617
{{{ 2x^2 + 7x + 3 = 0 }}}
The quadratic formula is
{{{x = ( -b +- sqrt( b^2-4*a*c ))/(2*a) }}}
The discriminant is
{{{ b^2 - 4*a*c }}}
and
{{{ a = 2 }}}
{{{ b = 7 }}}
{{{ c = 3 }}}
{{{ b^2 -  4*a*c = 7^2 - 4*2*3 }}}
{{{ b^2 - 4*a*c =  49 - 24 }}}
{{{ b^2 - 4*a*c = 25 }}}
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If the discriminant is positive, there are 2 real roots
{{{ x = ( -b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ x = ( -7 +- sqrt( 25 ))/(2*2) }}}
{{{ x = ( -7 + 5 )/4 }}}
{{{ x = -1/2 }}}
and, taking the negative square root of {{{ 25 }}},
{{{ x = ( -7 - sqrt( 25 ))/(2*2) }}}
{{{ x = ( -7 - 5 )/4 }}}
{{{ x = -12/4 }}}
{{{ x = -3 }}}
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From these results, I can write the factors
{{{ ( x + 1/2 )*( x +3 ) = 0 }}}
{{{ x^2 + (1/2)*x + 3x + 3/2 = 0 }}}
{{{ x^2 + (7/2)*x + 3/2 = 0 }}}
Multiply both sides by {{{ 2 }}}
{{{ 2x^2 + 7x + 3 = 0 }}}
OK