+0  
 
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Solve th following quadratic equations using any method. 

 

10,000x– 64 = 0

 

9x– 8 = — 34x

 

2x2 — 4x + 7 = 0 

 

3.2x + 0.2x— 5 = 0

Thank you! 

FieryJade122  Apr 10, 2018
 #1
avatar+3 
+2

1. We can move 64 to the other side to get 10,000\(x^2\)=64. We then divide both sides by 10,000 to get 64/10000=\(x^2\)

we can then square root both sides to get 8/100=2/25. 

2. We move 34x to the right side to get 9x^2+34x-8=0 you can then use the quadratic formula(or factor, I was just too lazy) to get x=-4, 2/9

3. You can also use the quadratic formula to get imaginary solutions. There are no real solutions to this one. 

4. You can also use the quadratic formula to get -3.2 plus minus \( \sqrt{14.24}\) all over 4. 

DMISO  Apr 10, 2018
 #2
avatar+92367 
+1

10000x^2  - 64   =  0       factor as a difference of squares

(100x - 8) (100x + 8)  = 0

Set both factors to 0  and solve for x

 

100x  - 8   =  0                    100x  + 8  = 0              

100x  = 8                             100x  =  - 8

x  = 8/100  =  2/25                x  =  -8/100  =  -2/25

 

 

9x^2  - 8  =  -34        rearrange  as

 

9x^2 + 34x - 8  =  0    factor

(9x - 2) (x + 4)  =  0

Set both factors to 0  and solve for   x

9x - 2  = 0                 x  +  4  =  0

9x  =  2                      x =  - 4          

x  = 2/9

 

 

2x^2 - 4x + 7  = 0     us the quadratic formula

 

 

x  =    4 ± √ [ 4^2 - 4*2* 7 ]           4  ± √ [-40]           4  ± 2 i√ 10

         ________________   =     __________   =    _________  =

              2 (2)                                    4                            4

 

 

2  ± i√10

_______

    2

 

 

3.2x + 0.2x^2 - 5  = 0      rearrange

 

0.2x^2 + 3.2x - 5  =  0     multiply through by 10

 

2x^2 + 32x - 50  = 0        divide through by 2

 

x^2 + 16x - 25  =  0       complete the square on x

 

x^2 + 16x + 64  =  25 + 64

 

(x + 8)^2  =  89         take both rots

 

x + 8   =   ± √89

 

x  =   ± √89  - 8

 

 

cool cool cool

CPhill  Apr 10, 2018
 #3
avatar+23 
+1

Thank you guys sooo much! That really helped!laugh

FieryJade122  Apr 10, 2018
 #4
avatar
0

8/100 and -8/100

Guest Apr 10, 2018

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