Solve x^3-x^2 = (x-1)3

Question

Solve the equation

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

Alternative Form

x_{1} \approx - 1.732051, x_{2} = 1, x_{3} \approx 1.732051

Evaluate

x^{3} - x^{2} = (x - 1) \times 3

Multiply the terms

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

Move the expression to the left side

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

Calculate

More Steps

Evaluate

- 3 (x - 1)

Apply the distributive property

- 3 x - (- 3 \times 1)

Any expression multiplied by 1 remains the same

- 3 x - (- 3)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 3 x + 3

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

Factor the expression

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

Separate the equation into 2 possible cases

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

Solve the equation

More Steps

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} - 3 = 0

Solve the equation

More Steps

Evaluate

x^{2} - 3 = 0

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

x^{2} = 0 + 3

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

x^{2} = 3

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

x = \pm 3

Separate the equation into 2 possible cases

x = 3 x = - 3

x = 1 x = 3 x = - 3

Solution

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

Alternative Form

x_{1} \approx - 1.732051, x_{2} = 1, x_{3} \approx 1.732051

Show Solution

Solve the equation

Graph