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Completing the square: smallest value if the variable is real?
I've completed the square for x^2 + 5x + 4, giving me (x+5/2)^2 - 9/4 but I am then asked what is the smallest value if the variable is real. Does this just mean if x=1 because then it doesn't even require that I complete the square
You got x² + 5x + 4 = (x + 5/2)² - 9/4
and they want you to find the smallest possible value.
Notice that the smallest possible value of (x + 5/2)² must be 0 because it can never be a negative number. Hence the smallest possible value of x² + 5x + 4 is 0 - 9/4 = -9/4.
There is actually more that you can say. You know that the smallest value of x² + 5x + 4 occurs when x = -5/2 because x = -5/2 is what makes (x + 5/2)² equal to 0.
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