Solve (x^2 x-6)^2 (x^2-9)^2=0

Question

Solve the equation

x_{1} = - 3, x_{2} = 36, x_{3} = 3

Alternative Form

x_{1} = - 3, x_{2} \approx 1.817121, x_{3} = 3

Evaluate

(x^{2} \times x - 6)^{2} (x^{2} - 9)^{2} = 0

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} - 6)^{2} (x^{2} - 9)^{2} = 0

Separate the equation into 2 possible cases

(x^{3} - 6)^{2} = 0 (x^{2} - 9)^{2} = 0

Solve the equation

More Steps

Evaluate

(x^{3} - 6)^{2} = 0

The only way a power can be 0 is when the base equals 0

x^{3} - 6 = 0

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

x^{3} = 0 + 6

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

x^{3} = 6

Take the 3 -th root on both sides of the equation

3 x^{3} = 36

Calculate

x = 36

x = 36 (x^{2} - 9)^{2} = 0

Solve the equation

More Steps

Evaluate

(x^{2} - 9)^{2} = 0

The only way a power can be 0 is when the base equals 0

x^{2} - 9 = 0

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

x^{2} = 0 + 9

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

x^{2} = 9

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

x = \pm 9

Simplify the expression

More Steps

Evaluate

9

Write the number in exponential form with the base of 3

3^{2}

Reduce the index of the radical and exponent with 2

3

x = \pm 3

Separate the equation into 2 possible cases

x = 3 x = - 3

x = 36 x = 3 x = - 3

Solution

x_{1} = - 3, x_{2} = 36, x_{3} = 3

Alternative Form

x_{1} = - 3, x_{2} \approx 1.817121, x_{3} = 3

Show Solution