Question 433393
These are in the form {{{ ax^2 + bx + c = 0 }}}
The discriminant is {{{b^2 - 4*a*c }}}
(1)
{{{  4x^2 - 4x + 1 = 0 }}}
{{{ b^2 - 4*a*c = (-4)^2 - 4*4*1 }}}
{{{ 16 - 16 = 0 }}}
When the discriminant is {{{0}}}, there is one real solution
Which is {{{ (-b)/2a  = -(-4) / (2*4) }}}
{{{ x = 1/2 }}}
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(2)
The discriminant is {{{ (-6)^2 - 4*1*7 = 36 - 28 }}}
{{{ 36 - 28 = 8 }}}
There are 2 real solutions which are
{{{ (-(-6) + sqrt(8) ) / (2*1) }}}
{{{ x = 3 + sqrt(2) }}}
and
{{{ (-(-6) - sqrt(8) ) / (2*1) }}}
{{{ x = 3 - sqrt(2) }}}