IM Alg2.3.17 Practice: Completing the Square and Complex Solutions

Find the solution or solutions to each equation.
[math]x^2+0.5x-14=0[/math]
[math]x^2+12x+36=0[/math]
[math]x^2-3x+8=0[/math]
[math]x^2+4=0[/math]
[size=150]Which describes the solutions to the equation [math]x^2+7=0[/math]?[/size]
[size=150]Explain how you know [math]\sqrt{3x+2}=\text{-}16[/math] has no solutions.[/size]
Here is an applet of some graphs.
Using the applet above, determine the number of real solutions and non-real solutions to each equation. Use the graphs; don't do any calculations to find the solutions.
[math]x^2-6x+7=0[/math]
[math]3x^2+2x+1=0[/math]
[math]\text{-}x^2-3x+2=0[/math]
[math]x^2-6x+7=\text{-}2[/math]
[math]\text{-}x^2-3x+2=6[/math]
[math]3x^2+2x+1=2[/math]
[size=150]Write [math](5-5i)^2[/math] in the form [math]a+bi[/math], where [math]a[/math] and [math]b[/math] are real numbers.[br][/size]
[size=150]Write [math](5-5i)^4[/math] in the form [math]a+bi[/math], where [math]a[/math] and [math]b[/math] are real numbers.[br][/size]
What number n makes this equation true?
[math]x^2+11x+\frac{121}{4}=(x+n)^2[/math]
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– GeoGebra Classroom Activities, IM Algebra 1, Geometry, Algebra 2

Information: IM Alg2.3.17 Practice: Completing the Square and Complex Solutions