Solve x^2(x-15)=2*(x-15)

Question

Solve the equation

x_{1} = - 2, x_{2} = 2, x_{3} = 15

Alternative Form

x_{1} \approx - 1.414214, x_{2} \approx 1.414214, x_{3} = 15

Evaluate

x^{2} (x - 15) = 2 (x - 15)

Calculate

More Steps

Evaluate

x^{2} (x - 15)

Apply the distributive property

x^{2} \times x - x^{2} \times 15

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 15

Use the commutative property to reorder the terms

x^{3} - 15 x^{2}

x^{3} - 15 x^{2} = 2 (x - 15)

Calculate

More Steps

Evaluate

2 (x - 15)

Apply the distributive property

2 x - 2 \times 15

Multiply the numbers

2 x - 30

x^{3} - 15 x^{2} = 2 x - 30

Move the expression to the left side

x^{3} - 15 x^{2} - (2 x - 30) = 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} - 15 x^{2} - 2 x + 30 = 0

Factor the expression

(x - 15) (x^{2} - 2) = 0

Separate the equation into 2 possible cases

x - 15 = 0 x^{2} - 2 = 0

Solve the equation

More Steps

Evaluate

x - 15 = 0

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

x = 0 + 15

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

x = 15

x = 15 x^{2} - 2 = 0

Solve the equation

More Steps

Evaluate

x^{2} - 2 = 0

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

x^{2} = 0 + 2

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

x^{2} = 2

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

x = \pm 2

Separate the equation into 2 possible cases

x = 2 x = - 2

x = 15 x = 2 x = - 2

Solution

x_{1} = - 2, x_{2} = 2, x_{3} = 15

Alternative Form

x_{1} \approx - 1.414214, x_{2} \approx 1.414214, x_{3} = 15

Show Solution

Solve the equation

Graph