# Chapter 8 - Sections 8.1-8.3 - Integrated Review - Summary on Solving Quadratic Equations: 12

$x=\dfrac{-1\pm i\sqrt{11}}{2}$

#### Work Step by Step

Using the properties of equality, the given quadratic equation, $x^2+x=-3 ,$ is equivalent to \begin{array}{l}\require{cancel} x^2+x+3=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{-1\pm\sqrt{1^2-4(1)(3)}}{2(1)} \\\\ x=\dfrac{-1\pm\sqrt{1-12}}{2} \\\\ x=\dfrac{-1\pm\sqrt{-11}}{2} \\\\ x=\dfrac{-1\pm\sqrt{-1}\cdot\sqrt{11}}{2} \\\\ x=\dfrac{-1\pm i\sqrt{11}}{2} .\end{array}

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