Each solution to $x^2 + 5x + 8 = 0$ can be written in the form $x = a + b i,$ where $a$ and $b$ are real numbers. What is $a + b^2$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Each solution to $x^2 + 5x + 8 = 0$ can be written in the form $x = a + b i,$ where $a$ and $b$ are real numbers. What is $a + b^2$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
-\dfrac{3}{4}
Each solution to $x^2 + 5x + 8 = 0$ can be written in the form $x = a + b i,$ where $a$ and $b$ are real numbers. What is $a + b^2$?
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