Solve 11/12(-2x^6)-1/2

Question

Simplify the expression

- \frac{11}{6} x^{6} - \frac{1}{2}

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- \frac{1}{6} (11 x^{6} + 3)

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x_{1} = - \frac{6 81 \times 1 1 ^{5}}{22} - \frac{6 3 \times 1 1 ^{5}}{22} i, x_{2} = \frac{6 81 \times 1 1 ^{5}}{22} + \frac{6 3 \times 1 1 ^{5}}{22} i

Alternative Form

x_{1} \approx - 0.697406 - 0.402647 i, x_{2} \approx 0.697406 + 0.402647 i

Evaluate

\frac{11}{12} (- 2 x^{6}) - \frac{1}{2}

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

\frac{11}{12} (- 2 x^{6}) - \frac{1}{2} = 0

Multiply the numbers

More Steps

- \frac{11}{6} x^{6} - \frac{1}{2} = 0

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

- \frac{11}{6} x^{6} = 0 + \frac{1}{2}

Add the terms

- \frac{11}{6} x^{6} = \frac{1}{2}

Change the signs on both sides of the equation

\frac{11}{6} x^{6} = - \frac{1}{2}

Multiply by the reciprocal

\frac{11}{6} x^{6} \times \frac{6}{11} = - \frac{1}{2} \times \frac{6}{11}

Multiply

x^{6} = - \frac{1}{2} \times \frac{6}{11}

Multiply

More Steps

x^{6} = - \frac{3}{11}

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

x = \pm 6 - \frac{3}{11}

Simplify the expression

More Steps

x = \pm (\frac{6 81 \times 1 1 ^{5}}{22} + \frac{6 3 \times 1 1 ^{5}}{22} i)

Separate the equation into 2 possible cases

x = \frac{6 81 \times 1 1 ^{5}}{22} + \frac{6 3 \times 1 1 ^{5}}{22} i x = - \frac{6 81 \times 1 1 ^{5}}{22} - \frac{6 3 \times 1 1 ^{5}}{22} i

Solution

x_{1} = - \frac{6 81 \times 1 1 ^{5}}{22} - \frac{6 3 \times 1 1 ^{5}}{22} i, x_{2} = \frac{6 81 \times 1 1 ^{5}}{22} + \frac{6 3 \times 1 1 ^{5}}{22} i

Alternative Form

x_{1} \approx - 0.697406 - 0.402647 i, x_{2} \approx 0.697406 + 0.402647 i

Show Solution