Solve (x-2)(x^2)=7x-14

Question

Solve the equation

x_{1} = - 7, x_{2} = 2, x_{3} = 7

Alternative Form

x_{1} \approx - 2.645751, x_{2} = 2, x_{3} \approx 2.645751

Evaluate

(x - 2) x^{2} = 7 x - 14

Multiply the terms

x^{2} (x - 2) = 7 x - 14

Expand the expression

More Steps

Evaluate

x^{2} (x - 2)

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

x^{2} \times x

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{2 + 1}

Add the numbers

x^{3}

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

Use the commutative property to reorder the terms

x^{3} - 2 x^{2}

x^{3} - 2 x^{2} = 7 x - 14

Move the expression to the left side

x^{3} - 2 x^{2} - (7 x - 14) = 0

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

x^{3} - 2 x^{2} - 7 x + 14 = 0

Factor the expression

(x - 2) (x^{2} - 7) = 0

Separate the equation into 2 possible cases

x - 2 = 0 x^{2} - 7 = 0

Solve the equation

More Steps

Evaluate

x - 2 = 0

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

x = 0 + 2

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

x = 2

x = 2 x^{2} - 7 = 0

Solve the equation

More Steps

Evaluate

x^{2} - 7 = 0

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

x^{2} = 0 + 7

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

x^{2} = 7

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

x = \pm 7

Separate the equation into 2 possible cases

x = 7 x = - 7

x = 2 x = 7 x = - 7

Solution

x_{1} = - 7, x_{2} = 2, x_{3} = 7

Alternative Form

x_{1} \approx - 2.645751, x_{2} = 2, x_{3} \approx 2.645751

Show Solution

Solve the equation

Graph