Solve (-5x^52x^4-1/3x^3) (-1/2x^3) - ScanMath

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Question

Simplify the expression

5 x^{12} + \frac{1}{6} x^{6}

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Factor the expression

\frac{1}{6} x^{6} (30 x^{6} + 1)

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Find the roots

x_{1} = - \frac{6 810 \times 90 0 ^{2}}{60} + \frac{6 3 0 ^{5}}{60} i, x_{2} = \frac{6 810 \times 90 0 ^{2}}{60} - \frac{6 3 0 ^{5}}{60} i, x_{3} = 0

Alternative Form

x_{1} \approx - 0.491297 + 0.28365 i, x_{2} \approx 0.491297 - 0.28365 i, x_{3} = 0

Evaluate

(- 5 x^{5} \times 2 x^{4} - \frac{1}{3} x^{3}) (- \frac{1}{2} x^{3})

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

(- 5 x^{5} \times 2 x^{4} - \frac{1}{3} x^{3}) (- \frac{1}{2} x^{3}) = 0

Multiply

More Steps

(- 10 x^{9} - \frac{1}{3} x^{3}) (- \frac{1}{2} x^{3}) = 0

Multiply the terms

- \frac{1}{2} x^{3} (- 10 x^{9} - \frac{1}{3} x^{3}) = 0

Change the sign

\frac{1}{2} x^{3} (- 10 x^{9} - \frac{1}{3} x^{3}) = 0

Elimination the left coefficient

x^{3} (- 10 x^{9} - \frac{1}{3} x^{3}) = 0

Separate the equation into 2 possible cases

x^{3} = 0 - 10 x^{9} - \frac{1}{3} x^{3} = 0

The only way a power can be 0 is when the base equals 0

x = 0 - 10 x^{9} - \frac{1}{3} x^{3} = 0

Solve the equation

More Steps

x = 0 x = 0 x = \frac{6 810 \times 90 0 ^{2}}{60} - \frac{6 3 0 ^{5}}{60} i x = - \frac{6 810 \times 90 0 ^{2}}{60} + \frac{6 3 0 ^{5}}{60} i

Find the union

x = 0 x = \frac{6 810 \times 90 0 ^{2}}{60} - \frac{6 3 0 ^{5}}{60} i x = - \frac{6 810 \times 90 0 ^{2}}{60} + \frac{6 3 0 ^{5}}{60} i

Solution

x_{1} = - \frac{6 810 \times 90 0 ^{2}}{60} + \frac{6 3 0 ^{5}}{60} i, x_{2} = \frac{6 810 \times 90 0 ^{2}}{60} - \frac{6 3 0 ^{5}}{60} i, x_{3} = 0

Alternative Form

x_{1} \approx - 0.491297 + 0.28365 i, x_{2} \approx 0.491297 - 0.28365 i, x_{3} = 0

Show Solution