Question 1166286
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1)  {{{ 4x^2-x-8 = 0 }}}

Divide both sides by 4:
     {{{ x^2-(1/4)x-2 = 0 }}}

Add 2 both sides:
      {{{ x^2 - (1/4)x = 2 }}}
  
Add {{{ ((1/2)(1/4))^2 = 1/64 }}} to both sides:
      {{{ x^2 -(1/4)x + 1/64 = 2 + 1/64 }}}

Simplify RHS: 
    {{{ x^2 -(1/4)x + 1/64 = 129/64 }}}

Notice LHS is perfect square:
    {{{ (x-1/8)^2 = 129/64 }}} 

Take sqrt both sides, use +/- on RHS (b/c LHS^2 = RHS^2 we otherwise would lose the negative solution):
     {{{  (x-1/8) }}} = +- {{{ sqrt(129/64) }}}

Add 1/8 to both sides:
     {{{  x = (1/8) +- sqrt(129/64) }}}

This can be written:
     {{{ x = (1 +- sqrt(129))/8 }}}

Note that there are two solutions, agreeing with the highest power of the polynomial (2).



The others are procedurally the same.