Solve (2x^3)^2-4(2x^3)-12=0

Question

Solve the equation

x_{1} = - 1, x_{2} = 33

Alternative Form

x_{1} = - 1, x_{2} \approx 1.44225

Evaluate

(2 x^{3})^{2} - 4 \times 2 x^{3} - 12 = 0

Simplify

More Steps

Evaluate

(2 x^{3})^{2} - 4 \times 2 x^{3} - 12

Multiply the numbers

(2 x^{3})^{2} - 8 x^{3} - 12

Rewrite the expression

More Steps

Evaluate

(2 x^{3})^{2}

To raise a product to a power,raise each factor to that power

2^{2} (x^{3})^{2}

Evaluate the power

4 (x^{3})^{2}

Evaluate the power

4 x^{6}

4 x^{6} - 8 x^{3} - 12

4 x^{6} - 8 x^{3} - 12 = 0

Factor the expression

4 (x + 1) (x^{2} - x + 1) (x^{3} - 3) = 0

Divide both sides

(x + 1) (x^{2} - x + 1) (x^{3} - 3) = 0

Separate the equation into 3 possible cases

x + 1 = 0 x^{2} - x + 1 = 0 x^{3} - 3 = 0

Solve the equation

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Evaluate

x + 1 = 0

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

x = 0 - 1

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

x = - 1

x = - 1 x^{2} - x + 1 = 0 x^{3} - 3 = 0

Solve the equation

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Evaluate

x^{2} - x + 1 = 0

Substitute a= 1,b= - 1 and c= 1 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{1 \pm ( - 1 ) ^{2} - 4}{2}

Simplify the expression

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Evaluate

(- 1)^{2} - 4

Evaluate the power

1 - 4

Subtract the numbers

- 3

x = \frac{1 \pm - 3}{2}

The expression is undefined in the set of real numbers

x \in / R

x = - 1 x \in / R x^{3} - 3 = 0

Solve the equation

More Steps

Evaluate

x^{3} - 3 = 0

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

x^{3} = 0 + 3

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

x^{3} = 3

Take the 3 -th root on both sides of the equation

3 x^{3} = 33

Calculate

x = 33

x = - 1 x \in / R x = 33

Find the union

x = - 1 x = 33

Solution

x_{1} = - 1, x_{2} = 33

Alternative Form

x_{1} = - 1, x_{2} \approx 1.44225

Show Solution