Solve 2x^3-24x 107

Question

Simplify the expression

2 x^{3} - 2568 x

Evaluate

2 x^{3} - 24 x \times 107

Solution

2 x^{3} - 2568 x

Show Solution

2 x (x^{2} - 1284)

Evaluate

2 x^{3} - 24 x \times 107

Multiply the terms

2 x^{3} - 2568 x

Rewrite the expression

2 x \times x^{2} - 2 x \times 1284

Solution

2 x (x^{2} - 1284)

Show Solution

x_{1} = - 2321, x_{2} = 0, x_{3} = 2321

Alternative Form

x_{1} \approx - 35.832946, x_{2} = 0, x_{3} \approx 35.832946

Evaluate

2 x^{3} - 24 x \times 107

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

2 x^{3} - 24 x \times 107 = 0

Multiply the terms

2 x^{3} - 2568 x = 0

Factor the expression

2 x (x^{2} - 1284) = 0

Divide both sides

x (x^{2} - 1284) = 0

Separate the equation into 2 possible cases

x = 0 x^{2} - 1284 = 0

Solve the equation

More Steps

Evaluate

x^{2} - 1284 = 0

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

x^{2} = 0 + 1284

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

x^{2} = 1284

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 1284

Simplify the expression

More Steps

Evaluate

1284

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 321

Write the number in exponential form with the base of 2

2^{2} \times 321

The root of a product is equal to the product of the roots of each factor

2^{2} \times 321

Reduce the index of the radical and exponent with 2

2321

x = \pm 2321

Separate the equation into 2 possible cases

x = 2321 x = - 2321

x = 0 x = 2321 x = - 2321

Solution

x_{1} = - 2321, x_{2} = 0, x_{3} = 2321

Alternative Form

x_{1} \approx - 35.832946, x_{2} = 0, x_{3} \approx 35.832946

Show Solution