Question 1119891
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<pre>
You want to solve an inequality


    16x^2 + 1 >= -8x.


It is equivalent to


    16x^2 + 8x + 1 >= 0.


It is equivalent to


    {{{(4x+1)^2}}} >= 0.


The last inequality is valid <U>for all real values x</U>.


<U>Answer</U>.  The given inequality has the set of solutions ALL REAL NUMBERS.



  {{{graph( 330, 330, -2.5, 2.5, -5.5, 40.5,
          16x^2 + 8x + 1
)}}}


        Plot y = {{{16x^2 + 8x + 1}}}
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<U>Be aware</U> :  &nbsp;&nbsp;The solution by &nbsp;@rapture1965 &nbsp;is &nbsp;&nbsp;<U>I N C O R R E C T</U>.