Solve (3x^2 2x-8)-(-x^2 6x^4)

Question

Simplify the expression

6 x^{3} - 8 + 6 x^{6}

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2 (3 x^{3} - 4 + 3 x^{6})

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x_{1} = - \frac{3 108 + 36 57}{6}, x_{2} = \frac{3 - 108 + 36 57}{6}

Alternative Form

x_{1} \approx - 1.206975, x_{2} \approx 0.911902

Evaluate

(3 x^{2} \times 2 x - 8) - (- x^{2} \times 6 x^{4})

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

(3 x^{2} \times 2 x - 8) - (- x^{2} \times 6 x^{4}) = 0

Multiply

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(6 x^{3} - 8) - (- x^{2} \times 6 x^{4}) = 0

Remove the parentheses

6 x^{3} - 8 - (- x^{2} \times 6 x^{4}) = 0

Multiply

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6 x^{3} - 8 - (- 6 x^{6}) = 0

Rewrite the expression

6 x^{3} - 8 + 6 x^{6} = 0

Solve the equation using substitution t = x^{3}

6 t - 8 + 6 t^{2} = 0

Rewrite in standard form

6 t^{2} + 6 t - 8 = 0

Substitute a= 6,b= 6 and c= - 8 into the quadratic formula t = \frac{- b \pm b ^{2} - 4 a c}{2 a}

t = \frac{- 6 \pm 6 ^{2} - 4 \times 6 ( - 8 )}{2 \times 6}

Simplify the expression

t = \frac{- 6 \pm 6 ^{2} - 4 \times 6 ( - 8 )}{12}

Simplify the expression

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t = \frac{- 6 \pm 228}{12}

Simplify the radical expression

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t = \frac{- 6 \pm 2 57}{12}

Separate the equation into 2 possible cases

t = \frac{- 6 + 2 57}{12} t = \frac{- 6 - 2 57}{12}

Simplify the expression

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t = \frac{- 3 + 57}{6} t = \frac{- 6 - 2 57}{12}

Simplify the expression

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t = \frac{- 3 + 57}{6} t = - \frac{3 + 57}{6}

Substitute back

x^{3} = \frac{- 3 + 57}{6} x^{3} = - \frac{3 + 57}{6}

Solve the equation for x

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x = \frac{3 - 108 + 36 57}{6} x^{3} = - \frac{3 + 57}{6}

Solve the equation for x

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x = \frac{3 - 108 + 36 57}{6} x = - \frac{3 108 + 36 57}{6}

Solution

x_{1} = - \frac{3 108 + 36 57}{6}, x_{2} = \frac{3 - 108 + 36 57}{6}

Alternative Form

x_{1} \approx - 1.206975, x_{2} \approx 0.911902

Show Solution