Solve (-5x^46x^2-43) (6x^4-x^212x 12) - ScanMath

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Type your math problem... (-5x^46x^2-43) (6x^4-x^212x 12)

Question

Simplify the expression

- 180 x^{10} + 4320 x^{9} - 258 x^{4} + 6192 x^{3}

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Factor the expression

- 6 x^{3} (30 x^{6} + 43) (x - 24)

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Find the roots

x_{1} = 0, x_{2} = 24, x_{3} = - \frac{6 387 \times 1 0 ^{5}}{20} - \frac{6 43 \times 3 0 ^{5}}{60} i, x_{4} = \frac{6 387 \times 1 0 ^{5}}{20} + \frac{6 43 \times 3 0 ^{5}}{60} i

Alternative Form

x_{1} = 0, x_{2} = 24, x_{3} \approx - 0.919578 - 0.530919 i, x_{4} \approx 0.919578 + 0.530919 i

Evaluate

(- 5 x^{4} \times 6 x^{2} - 43) (6 x^{4} - x^{2} \times 12 x \times 12)

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

(- 5 x^{4} \times 6 x^{2} - 43) (6 x^{4} - x^{2} \times 12 x \times 12) = 0

Multiply

More Steps

(- 30 x^{6} - 43) (6 x^{4} - x^{2} \times 12 x \times 12) = 0

Multiply

More Steps

(- 30 x^{6} - 43) (6 x^{4} - 144 x^{3}) = 0

Change the sign

(30 x^{6} + 43) (6 x^{4} - 144 x^{3}) = 0

Separate the equation into 2 possible cases

30 x^{6} + 43 = 0 6 x^{4} - 144 x^{3} = 0

Solve the equation

More Steps

x = \frac{6 387 \times 1 0 ^{5}}{20} + \frac{6 43 \times 3 0 ^{5}}{60} i x = - \frac{6 387 \times 1 0 ^{5}}{20} - \frac{6 43 \times 3 0 ^{5}}{60} i 6 x^{4} - 144 x^{3} = 0

Solve the equation

More Steps

x = \frac{6 387 \times 1 0 ^{5}}{20} + \frac{6 43 \times 3 0 ^{5}}{60} i x = - \frac{6 387 \times 1 0 ^{5}}{20} - \frac{6 43 \times 3 0 ^{5}}{60} i x = 0 x = 24

Solution

x_{1} = 0, x_{2} = 24, x_{3} = - \frac{6 387 \times 1 0 ^{5}}{20} - \frac{6 43 \times 3 0 ^{5}}{60} i, x_{4} = \frac{6 387 \times 1 0 ^{5}}{20} + \frac{6 43 \times 3 0 ^{5}}{60} i

Alternative Form

x_{1} = 0, x_{2} = 24, x_{3} \approx - 0.919578 - 0.530919 i, x_{4} \approx 0.919578 + 0.530919 i

Show Solution