Solve 12a^3-7a^3-5a-18a^3 9a^2 56

Question

Simplify the expression

5 a^{3} - 5 a - 9072 a^{5}

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a (5 a^{2} - 5 - 9072 a^{4})

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a = 0

Evaluate

12 a^{3} - 7 a^{3} - 5 a - 18 a^{3} \times 9 a^{2} \times 56

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

12 a^{3} - 7 a^{3} - 5 a - 18 a^{3} \times 9 a^{2} \times 56 = 0

Subtract the terms

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5 a^{3} - 5 a - 18 a^{3} \times 9 a^{2} \times 56 = 0

Multiply

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5 a^{3} - 5 a - 9072 a^{5} = 0

Factor the expression

a (5 a^{2} - 5 - 9072 a^{4}) = 0

Separate the equation into 2 possible cases

a = 0 5 a^{2} - 5 - 9072 a^{4} = 0

Solve the equation

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Evaluate

5 a^{2} - 5 - 9072 a^{4} = 0

Solve the equation using substitution t = a^{2}

5 t - 5 - 9072 t^{2} = 0

Rewrite in standard form

- 9072 t^{2} + 5 t - 5 = 0

Multiply both sides

9072 t^{2} - 5 t + 5 = 0

Substitute a= 9072,b= - 5 and c= 5 into the quadratic formula t = \frac{- b \pm b ^{2} - 4 a c}{2 a}

t = \frac{5 \pm ( - 5 ) ^{2} - 4 \times 9072 \times 5}{2 \times 9072}

Simplify the expression

t = \frac{5 \pm ( - 5 ) ^{2} - 4 \times 9072 \times 5}{18144}

Simplify the expression

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t = \frac{5 \pm - 181415}{18144}

Simplify the radical expression

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t = \frac{5 \pm 181415 \times i}{18144}

Separate the equation into 2 possible cases

t = \frac{5 + 181415 \times i}{18144} t = \frac{5 - 181415 \times i}{18144}

Simplify the expression

t = \frac{5}{18144} + \frac{181415}{18144} i t = \frac{5 - 181415 \times i}{18144}

Simplify the expression

t = \frac{5}{18144} + \frac{181415}{18144} i t = \frac{5}{18144} - \frac{181415}{18144} i

Substitute back

a^{2} = \frac{5}{18144} + \frac{181415}{18144} i a^{2} = \frac{5}{18144} - \frac{181415}{18144} i

Solve the equation for a

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a_{1} = \frac{4 1715 \times cos ( \frac{a r c t a n ( \frac{181415}{5} )}{2} )}{42} + \frac{4 1715 \times sin ( \frac{a r c t a n ( \frac{181415}{5} )}{2} )}{42} i a_{2} = \frac{4 1715 \times cos ( \frac{a r c t a n ( \frac{181415}{5} ) + 2 π}{2} )}{42} + \frac{4 1715 \times sin ( \frac{a r c t a n ( \frac{181415}{5} ) + 2 π}{2} )}{42} i a^{2} = \frac{5}{18144} - \frac{181415}{18144} i

Solve the equation for a

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a_{1} = \frac{4 1715 \times cos ( \frac{a r c t a n ( \frac{181415}{5} )}{2} )}{42} + \frac{4 1715 \times sin ( \frac{a r c t a n ( \frac{181415}{5} )}{2} )}{42} i a_{2} = \frac{4 1715 \times cos ( \frac{a r c t a n ( \frac{181415}{5} ) + 2 π}{2} )}{42} + \frac{4 1715 \times sin ( \frac{a r c t a n ( \frac{181415}{5} ) + 2 π}{2} )}{42} i a_{1} = - \frac{4 1715 \times cos ( - \frac{a r c t a n ( - \frac{181415}{5} )}{2} )}{42} + \frac{4 1715 \times sin ( \frac{a r c t a n ( - \frac{181415}{5} ) + 2 π}{2} )}{42} i a_{2} = \frac{4 1715 \times cos ( \frac{a r c t a n ( - \frac{181415}{5} ) + 2 π + 2 π}{2} )}{42} + \frac{4 1715 \times sin ( \frac{a r c t a n ( - \frac{181415}{5} ) + 2 π + 2 π}{2} )}{42} i

a = 0 a \in / R

Solution

a = 0

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