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Popular >

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

Solution

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

Solution

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

Solution steps

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

Multiply by LCM=

10

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

Simplify

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

Expand

20 x (3 - 4 x) - 2 (x - 2) : - 80 x^{2} + 58 x + 4

Expand

5 (x - \frac{x - 1}{2} + 3) : \frac{5 x}{2} + \frac{5}{2} + 15

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

Subtract

\frac{5}{2} + 15

from both sides

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

Simplify

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

Move

\frac{5 x}{2}

to the left side

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

Write in the standard form

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

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

Solve with the quadratic formula

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

Simplify

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

The solutions to the quadratic equation are:

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

Popular Examples

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\frac{1}{5}

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2 (x - 5)^{2} = 0

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