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+0  
 
-5
78
4
avatar+41 

Solve each one!

 Feb 22, 2019
edited by GAMEMASTERX40  Feb 22, 2019
 #1
avatar+18360 
+1

-x^2+4x-13 = 0

x^2 - 4x + 13 = 0      Use quadratic formula  

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)       a = 1  b  = -4   c = 13

 

 

Sustituting yields       4 +- sqrt( 16- 4*1*13)   /  2     =    2 +-sqrt (-36)/2    =  2 +-  3i

 

Think you can try the others?

 Feb 22, 2019
 #2
avatar+100571 
+3

b )  x^2 + 41 = -8x

 

x^2 + 8x  =  -41      complete the square on x

 

x^2 + 8x + 16  =   -41 + 16

 

(x + 4)^2 =   - 25      take both roots

 

x + 4 =  ±√-25

 

x + 4 = ± 5i      subtract 4 from both sides

 

x =   - 4 ± 5i

 

 

cool  cool cool

 Feb 22, 2019
 #3
avatar+100571 
+3

(c)

 

-9x^2 = 30x + 25   rearrange as

 

9x^2 + 30x + 25 = 0        we can factor this    !!!

 

(3x + 5) ( 3x + 5) = 0

 

Setting either factor to 0 and solving for x produces     x =  - 5/3

 

 

cool cool cool

 Feb 22, 2019
 #4
avatar+100571 
+3

Lastly ...

 

5 - 7x^2 = 3x + 4  rearrange as

 

7x^2  + 3x + 4 - 5 = 0  simplify

 

7x^2 + 3x - 1 = 0

 

Quad formula

 

 x =  (  -3 ±√  [ 3^2 - 4 (7) (-1) ]  )  / [ 2 * 7 ] 

 

x = ( - 3 ±√ 37 ) /  14

 

 

 

cool cool cool

 Feb 22, 2019

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