# Chapter 8 - Review Exercises - Page 409: 4

{$-\frac{3}{4}\pm\frac{\sqrt {23}}{4}i$}

#### Work Step by Step

Step 1: $x(2x+3)=-4$ Step 2: $2x^{2}+3x=-4$ Step 3: $2x^{2}+3x+4=0$ Step 4: Comparing $2x^{2}+3x+4=0$ to the standard form of a quadratic equation $ax^{2}+bx+c=0$; $a=2$, $b=3$ and $c=4$ Step 5: The quadratic formula is: $x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$ Step 6: Substituting the values of a,b and c in the formula: $x=\frac{-(3) \pm \sqrt {(3)^{2}-4(2)(4)}}{2(2)}$ Step 7: $x=\frac{-3 \pm \sqrt {9-32}}{4}$ Step 8: $x=\frac{-3 \pm \sqrt {-23}}{4}$ Step 9: $x=\frac{-3 \pm \sqrt {-1\times23}}{4}$ Step 10: $x=\frac{-3 \pm \sqrt {-1}\times\sqrt {23}}{4}$ Step 11: $x=\frac{-3 \pm i\times\sqrt {23}}{4}$ Step 12: $x=\frac{-3 \pm i\sqrt {23}}{4}$ Step 13: $x=-\frac{3}{4}\pm\frac{\sqrt {23}}{4}i$ Step 14: Therefore, the solution set is {$-\frac{3}{4}\pm\frac{\sqrt {23}}{4}i$}.

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