Solve -2k^36k^24k-12

Question

Simplify the expression

- 48 k^{6} - 12

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- 12 (4 k^{6} + 1)

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k_{1} = - \frac{6 432}{4} + \frac{3 4}{4} i, k_{2} = \frac{6 432}{4} - \frac{3 4}{4} i

Alternative Form

k_{1} \approx - 0.687365 + 0.39685 i, k_{2} \approx 0.687365 - 0.39685 i

Evaluate

- 2 k^{3} \times 6 k^{2} \times 4 k - 12

To find the roots of the expression,set the expression equal to 0

- 2 k^{3} \times 6 k^{2} \times 4 k - 12 = 0

Multiply

More Steps

- 48 k^{6} - 12 = 0

Move the constant to the right-hand side and change its sign

- 48 k^{6} = 0 + 12

Removing 0 doesn't change the value,so remove it from the expression

- 48 k^{6} = 12

Change the signs on both sides of the equation

48 k^{6} = - 12

Divide both sides

\frac{48 k ^{6}}{48} = \frac{- 12}{48}

Divide the numbers

k^{6} = \frac{- 12}{48}

Divide the numbers

More Steps

k^{6} = - \frac{1}{4}

Take the root of both sides of the equation and remember to use both positive and negative roots

k = \pm 6 - \frac{1}{4}

Simplify the expression

More Steps

k = \pm (\frac{6 432}{2 ^{2}} - \frac{3 4}{4} i)

Separate the equation into 2 possible cases

k = \frac{6 432}{2 ^{2}} - \frac{3 4}{4} i k = - \frac{6 432}{2 ^{2}} + \frac{3 4}{4} i

Calculate

k = \frac{6 432}{4} - \frac{3 4}{4} i k = - \frac{6 432}{2 ^{2}} + \frac{3 4}{4} i

Calculate

k = \frac{6 432}{4} - \frac{3 4}{4} i k = - \frac{6 432}{4} + \frac{3 4}{4} i

Solution

k_{1} = - \frac{6 432}{4} + \frac{3 4}{4} i, k_{2} = \frac{6 432}{4} - \frac{3 4}{4} i

Alternative Form

k_{1} \approx - 0.687365 + 0.39685 i, k_{2} \approx 0.687365 - 0.39685 i

Show Solution