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Popular >

x/3-1+(x^2)/2 =-2x^2+x-7/6

Solution

\frac{x}{3} - 1 + \frac{x ^{2}}{2} = - 2 x^{2} + x - \frac{7}{6}

Solution

x = \frac{2}{15} + i \frac{11}{15}, x = \frac{2}{15} - i \frac{11}{15}

Solution steps

\frac{x}{3} - 1 + \frac{x ^{2}}{2} = - 2 x^{2} + x - \frac{7}{6}

Find Least Common Multiplier of

3, 2, 6 : 6

Multiply by LCM=

6

\frac{x}{3} \cdot 6 - 1 \cdot 6 + \frac{x ^{2}}{2} \cdot 6 = - 2 x^{2} \cdot 6 + x \cdot 6 - \frac{7}{6} \cdot 6

Simplify

2 x - 6 + 3 x^{2} = - 12 x^{2} + 6 x - 7

Move

7

to the left side

3 x^{2} + 2 x + 1 = - 12 x^{2} + 6 x

Move

6 x

to the left side

3 x^{2} - 4 x + 1 = - 12 x^{2}

Move

12 x^{2}

to the left side

15 x^{2} - 4 x + 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 4 ) \pm ( - 4 ) ^{2} - 4 \cdot 15 \cdot 1}{2 \cdot 15}

Simplify

(- 4)^{2} - 4 \cdot 15 \cdot 1 : 211 i

x_{1, 2} = \frac{- ( - 4 ) \pm 2 11 i}{2 \cdot 15}

Separate the solutions

x_{1} = \frac{- ( - 4 ) + 2 11 i}{2 \cdot 15}, x_{2} = \frac{- ( - 4 ) - 2 11 i}{2 \cdot 15}

x = \frac{- ( - 4 ) + 2 11 i}{2 \cdot 15} : \frac{2}{15} + i \frac{11}{15}

x = \frac{- ( - 4 ) - 2 11 i}{2 \cdot 15} : \frac{2}{15} - i \frac{11}{15}

The solutions to the quadratic equation are:

x = \frac{2}{15} + i \frac{11}{15}, x = \frac{2}{15} - i \frac{11}{15}

Popular Examples

6 a^{2} + 5 a - 4 = 2

6 + x - x^{2} = x^{2}

(3 x + 4)^{2} = 8

m (m + 2) = - 3 - 2 m

completesquare 4x^2-24x+42 complete the square

4 x^{2} - 24 x + 42