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# Solve th following quadratic equations using any method.

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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!

Apr 10, 2018

#1
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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.

Apr 10, 2018
#2
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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

Apr 10, 2018
#3
+23
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Thank you guys sooo much! That really helped!