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العربية

2x(3-4x)-(x-2)/5 = 1/2 [x+3-(x-1)/2 ]

الحلّ

2 x (3 - 4 x) - \frac{x - 2}{5} = \frac{1}{2} [x + 3 - \frac{x - 1}{2}]

x = \frac{111}{320} - i \frac{3 551}{320}, x = \frac{111}{320} + i \frac{3 551}{320}

خطوات الحلّ

2 x (3 - 4 x) - \frac{x - 2}{5} = \frac{1}{2} [x + 3 - \frac{x - 1}{2}]

Find Least Common Multiplier of

5, 2 : 10

10 =

اضرب بالمضاعف المشترك الأصغر

2 x (3 - 4 x) \cdot 10 - \frac{x - 2}{5} \cdot 10 = \frac{1}{2} [x + 3 - \frac{x - 1}{2}] \cdot 10

بسّط

20 x (3 - 4 x) - 2 (x - 2) = 5 (x - \frac{x - 1}{2} + 3)

20 x (3 - 4 x) - 2 (x - 2)

وسّع:

- 80 x^{2} + 58 x + 4

5 (x - \frac{x - 1}{2} + 3)

وسّع:

\frac{5 x}{2} + \frac{5}{2} + 15

- 80 x^{2} + 58 x + 4 = \frac{5 x}{2} + \frac{5}{2} + 15

من الطرفين

\frac{5}{2} + 15

اطرح

- 80 x^{2} + 58 x + 4 - (\frac{5}{2} + 15) = \frac{5 x}{2} + \frac{5}{2} + 15 - (\frac{5}{2} + 15)

بسّط

- 80 x^{2} + 58 x - \frac{27}{2} = \frac{5 x}{2}

انقل

\frac{5 x}{2}

إلى الجانب الأيسر

\frac{- 160 x ^{2} + 111 x - 27}{2} = 0

a x^{2} + b x + c = 0

اكتب بالصورة الاعتياديّة

- 80 x^{2} + \frac{111 x}{2} - \frac{27}{2} = 0

حلّ بالاستعانة بالصيغة التربيعيّة

x_{1, 2} = \frac{- \frac{111}{2} \pm ( \frac{111}{2} ) ^{2} - 4 ( - 80 ) ( - \frac{27}{2} )}{2 ( - 80 )}

(\frac{111}{2})^{2} - 4 (- 80) (- \frac{27}{2})

بسّط:

i \frac{3 551}{2}

x_{1, 2} = \frac{- \frac{111}{2} \pm i \frac{3 551}{2}}{2 ( - 80 )}

Separate the solutions

x_{1} = \frac{- \frac{111}{2} + i \frac{3 551}{2}}{2 ( - 80 )}, x_{2} = \frac{- \frac{111}{2} - i \frac{3 551}{2}}{2 ( - 80 )}

x = \frac{- \frac{111}{2} + i \frac{3 551}{2}}{2 ( - 80 )} : \frac{111}{320} - i \frac{3 551}{320}

x = \frac{- \frac{111}{2} - i \frac{3 551}{2}}{2 ( - 80 )} : \frac{111}{320} + i \frac{3 551}{320}

حلول المعادلة التربيعيّة هي

x = \frac{111}{320} - i \frac{3 551}{320}, x = \frac{111}{320} + i \frac{3 551}{320}

s im pl i f y (3^{5})^{2}

x - 5 = - 3

l o n g m u lt 0.2 \cdot 10

3 (3 x + 1)^{2} - 12 = - 9

3 x + 2 > - 3