Question 574640
{{{ -16t^2 - 12t = 2 }}}
Divide both sides by {{{2}}}
{{{ -8t^2 - 6t = 1 }}}
Divide both sides by {{{ -8 }}}
{{{ t^2 + (3/4)*t = -(1/8) }}}
Complete the square
Take {{{ 1/2 }}} of the coefficient of {{{x}}},
square it, and add it to both sides
{{{ t^2 + (3/4)*t + (3/8)^2 = -(1/8) + (3/8)^2 }}}
{{{ ( t + 3/8 )^2 = -8/64 + 9/64 }}}
{{{ ( t + 3/8 )^2 = 1/64 }}}
take the square root of both sides ( both + and - roots )
{{{ t + 3/8 = 1/8 }}}
{{{ t = -(1/4) }}}
and
{{{ t + 3/8 = -(1/8) }}}
{{{ t = -(1/2) }}}
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check the answers:
{{{ -16t^2 - 12t = 2 }}}
{{{ -16(-1/4)^2 - 12*(-1/4) = 2 }}}
{{{ -1 + 3 = 2 }}}
{{{ 2 = 2 }}}
and
{{{ -16*(-1/2)^2 - 12*(-1/2) = 2 }}}
{{{ -4 + 6 = 2 }}}
{{{ 2 = 2 }}}
OK