Question 1032924
{{{ y = 4x^2 + 24x - 13 }}}
Set {{{  y = 0 }}} to find roots
{{{ 0 = 4x^2 + 24x - 13 }}}
Add {{{ 13 }}} to both sides
{{{ 4x^2 + 24x = 13 }}}
Divide both sides by {{{ 4 }}}
{{{ x^2 + 6x = 13/4 }}}
Take 1/2 of the coefficient of {{{ x }}},
square it and add it to both sides
{{{ x^2 + 6x + (6/2)^2 = 13/4 + (6/2)^2 }}}
Simplify
{{{ x^2 + 6x + 9 = 13/4 + 36/4 }}}
{{{ x^2 + 6x + 9 = 49/4 }}}
{{{ ( x + 3 )^2 = (7/2)^2 }}}
Take the ( positive ) square root of both sides
{{{ x + 3 = 7/2 }}}
{{{ x = 7/2 - 6/2 }}}
{{{ x = 1/2 }}}
Take the ( negative ) square root of both sides
{{{ x + 3 = -7/2 }}}
{{{ x = -6/2 - 7/2 }}}
{{{ x = -13/2 }}}
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check answers:
{{{ y = 4x^2 + 24x - 13 }}}
{{{ 0 = 4*(1/2)^2 + 24*(1/2) - 13 }}}
{{{ 0 = 4*(1/4) + 12 - 13 }}}
{{{ 0 = 1 + 12 - 13 }}}
{{{ 0 = 13 - 13 }}}
{{{ 0 = 0  }}}
and
{{{ y = 4x^2 + 24x - 13 }}}
{{{ 0 = 4*(-13/2)^2 + 24*(-13/2) - 13 }}}
{{{ 0 = 4*( 169/4 ) - 312/2 - 13 }}}
{{{ 0 = 169 - 156 - 13 }}}
{{{ 0 = 169 - 169 }}}
{{{ 0 = 0 }}}
OK