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1 .Find the solutions to \(x^2 + 64 = 0.\)

 

2. Find all the solutions to \( x^2 - 6x + 13 = 0.\)

 Jan 31, 2021
 #1
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x^2 +    64  = 0

 

x^2  = -64      take  both roots

 

x = ± √-64

 

x = ± 8i

 

 

x^2  - 6x   +   13  = 0 

 

x^2  - 6x      =   -13              complete the square on x

 

Take 1/2 of  6 =  3.....square it  = 9       add to both sides

 

x^2  - 6x  +  9   = -13   +  9      factor the left side, simplify the right

 

(x - 3)^2 =   -4                   take both roots

 

x - 3    ± √-4

 

x - 3   =  ± 2i              add 3 to both sides

 

x = ± 2i  +  3

 

 

cool cool cool

 Jan 31, 2021

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