Solve 4/5k=-2k 1/2 3/10k-2

Question

Solve the equation(The real numbers system)

k \in / R

Alternative Form

No real solution

Show Solution

Solve using the quadratic formula in the complex numbers system

Solve by completing the square in the complex numbers system

Solve using the PQ formula in the complex numbers system

k_{1} = - \frac{4}{3} - \frac{2 11}{3} i, k_{2} = - \frac{4}{3} + \frac{2 11}{3} i

Alternative Form

k_{1} \approx - 1. \dot{3} - 2.211083 i, k_{2} \approx - 1. \dot{3} + 2.211083 i

Evaluate

\frac{4}{5} k = - 2 k \times \frac{1}{2} \times \frac{3}{10} k - 2

Multiply

More Steps

\frac{4}{5} k = - \frac{3}{10} k^{2} - 2

Swap the sides

- \frac{3}{10} k^{2} - 2 = \frac{4}{5} k

Move the expression to the left side

- \frac{3}{10} k^{2} - 2 - \frac{4}{5} k = 0

Rewrite in standard form

- \frac{3}{10} k^{2} - \frac{4}{5} k - 2 = 0

Multiply both sides

\frac{3}{10} k^{2} + \frac{4}{5} k + 2 = 0

Multiply both sides

10 (\frac{3}{10} k^{2} + \frac{4}{5} k + 2) = 10 \times 0

Calculate

3 k^{2} + 8 k + 20 = 0

Substitute a= 3,b= 8 and c= 20 into the quadratic formula k = \frac{- b \pm b ^{2} - 4 a c}{2 a}

k = \frac{- 8 \pm 8 ^{2} - 4 \times 3 \times 20}{2 \times 3}

Simplify the expression

k = \frac{- 8 \pm 8 ^{2} - 4 \times 3 \times 20}{6}

Simplify the expression

More Steps

k = \frac{- 8 \pm - 176}{6}

Simplify the radical expression

More Steps

k = \frac{- 8 \pm 4 11 \times i}{6}

Separate the equation into 2 possible cases

k = \frac{- 8 + 4 11 \times i}{6} k = \frac{- 8 - 4 11 \times i}{6}

Simplify the expression

More Steps

k = - \frac{4}{3} + \frac{2 11}{3} i k = \frac{- 8 - 4 11 \times i}{6}

Simplify the expression

More Steps

k = - \frac{4}{3} + \frac{2 11}{3} i k = - \frac{4}{3} - \frac{2 11}{3} i

Solution

k_{1} = - \frac{4}{3} - \frac{2 11}{3} i, k_{2} = - \frac{4}{3} + \frac{2 11}{3} i

Alternative Form

k_{1} \approx - 1. \dot{3} - 2.211083 i, k_{2} \approx - 1. \dot{3} + 2.211083 i

Show Solution