Solve x^3 -67x 126

Question

Simplify the expression

x^{3} - 8442 x

Evaluate

x^{3} - 67 x \times 126

Solution

x^{3} - 8442 x

Show Solution

x (x^{2} - 8442)

Evaluate

x^{3} - 67 x \times 126

Multiply the terms

x^{3} - 8442 x

Rewrite the expression

x \times x^{2} - x \times 8442

Solution

x (x^{2} - 8442)

Show Solution

x_{1} = - 3938, x_{2} = 0, x_{3} = 3938

Alternative Form

x_{1} \approx - 91.880357, x_{2} = 0, x_{3} \approx 91.880357

Evaluate

x^{3} - 67 x \times 126

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

x^{3} - 67 x \times 126 = 0

Multiply the terms

x^{3} - 8442 x = 0

Factor the expression

x (x^{2} - 8442) = 0

Separate the equation into 2 possible cases

x = 0 x^{2} - 8442 = 0

Solve the equation

More Steps

Evaluate

x^{2} - 8442 = 0

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

x^{2} = 0 + 8442

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

x^{2} = 8442

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

x = \pm 8442

Simplify the expression

More Steps

Evaluate

8442

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

9 \times 938

Write the number in exponential form with the base of 3

3^{2} \times 938

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

3^{2} \times 938

Reduce the index of the radical and exponent with 2

3938

x = \pm 3938

Separate the equation into 2 possible cases

x = 3938 x = - 3938

x = 0 x = 3938 x = - 3938

Solution

x_{1} = - 3938, x_{2} = 0, x_{3} = 3938

Alternative Form

x_{1} \approx - 91.880357, x_{2} = 0, x_{3} \approx 91.880357

Show Solution