## Intermediate Algebra (6th Edition)

$x=\dfrac{-5\pm\sqrt{17}}{4}$
Using the properties of equality, the given quadratic equation, $2x^2=-5x-1 ,$ is equivalent to \begin{array}{l}\require{cancel} 2x^2+5x+1=0 .\end{array} Using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ or the Quadratic Formula, the solutions of the quadratic equation above are \begin{array}{l}\require{cancel} x=\dfrac{-5\pm\sqrt{(5)^2-4(2)(1)}}{2(2)} \\\\ x=\dfrac{-5\pm\sqrt{25-8}}{4} \\\\ x=\dfrac{-5\pm\sqrt{17}}{4} .\end{array}