Question 550663
{{{ x^2 - 7x = -6 }}}
Complete the square
{{{ x^2 - 7x + (7/2)^2 = -6 + (7/2)^2 }}}
{{{ x^2 - 7x + 49/4 = -24/4 + 49/4 }}}
{{{ ( x - 7/2 )^2 = 25/4 }}}
take the square root of both sides
{{{ x - 7/2 = 5/2 }}}
{{{ x = 12/2 }}}
{{{ x = 6 }}}
and, taking the negative square root,
{{{ x - 7/2 = -5/2 }}}
{{{ x = 2/2 }}}
{{{ x = 1 }}}
The solution set is (6,0) and (1,0)
check:
{{{ ( x - 6 )*( x - 1 ) = 0 }}}
{{{ ( x - 6 )*( x - 1 ) = x^2 - 7x + 6 }}}
{{{ x^2 - 7x + 6 = 0 }}}
{{{ x^2 - 7x = -6 }}}
OK