Question 583406
Is the problem to find the roots?
{{{ 2x^2-15x +7 = 0 }}}
Complete the square
{{{ 2x^2-15x  = -7 }}}
{{{ x^2 - (15/2)*x = -(7/2) }}}
{{{ x^2 - (15/2)*x + (15/4)^2 = -(7/2) + (15/4)^2 }}}
{{{ ( x - 15/4 )^2 = -(56/16) + 225/16 }}}
{{{ ( x - 15/4 )^2 = 169/16 }}
{{{ ( x - 15/4 )^2 = ( 13/4 )^2
Take the square root of both sides
{{{ x - 15/4 = 13/4 }}}
{{{ x = 28/4 }}}
{{{ x = 7 }}}
and also:
{{{ x - 15/4 = -(13/4) }}}
{{{ x = 2/4 }}}
{{{ x = 1/2 }}}
Rewrite these as:
{{{ x - 7 = 0 }}}
{{{ x - 1/2 = 0 }}}
{{{ ( x - 7 )*( x - 1/2 ) = 0 }}}
{{{ ( x - 7 )*( x - 1/2 ) = x^2 - 7x - (1/2)*x + 7/2 }}} answer
{{{ x^2 - (15/2)*x + 7/2 = 0 }}}
Multiply both sides by {{{2}}}
{{{ 2x^2 - 15x + 7 = 0 }}}
So, the factors are correct