Solve -t^3 4t^2 18t - 63

Question

Simplify the expression

- 72 t^{6} - 63

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- 9 (8 t^{6} + 7)

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t_{1} = - \frac{6 1512}{4} - \frac{6 56}{4} i, t_{2} = \frac{6 1512}{4} + \frac{6 56}{4} i

Alternative Form

t_{1} \approx - 0.846965 - 0.488995 i, t_{2} \approx 0.846965 + 0.488995 i

Evaluate

- t^{3} \times 4 t^{2} \times 18 t - 63

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

- t^{3} \times 4 t^{2} \times 18 t - 63 = 0

Multiply

More Steps

- 72 t^{6} - 63 = 0

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

- 72 t^{6} = 0 + 63

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

- 72 t^{6} = 63

Change the signs on both sides of the equation

72 t^{6} = - 63

Divide both sides

\frac{72 t ^{6}}{72} = \frac{- 63}{72}

Divide the numbers

t^{6} = \frac{- 63}{72}

Divide the numbers

More Steps

t^{6} = - \frac{7}{8}

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

t = \pm 6 - \frac{7}{8}

Simplify the expression

More Steps

t = \pm (\frac{6 1512}{4} + \frac{6 56}{4} i)

Separate the equation into 2 possible cases

t = \frac{6 1512}{4} + \frac{6 56}{4} i t = - \frac{6 1512}{4} - \frac{6 56}{4} i

Solution

t_{1} = - \frac{6 1512}{4} - \frac{6 56}{4} i, t_{2} = \frac{6 1512}{4} + \frac{6 56}{4} i

Alternative Form

t_{1} \approx - 0.846965 - 0.488995 i, t_{2} \approx 0.846965 + 0.488995 i

Show Solution