Solve (x^4-18x^2)

Question

Factor the expression

x^{2} (x^{2} - 18)

Evaluate

x^{4} - 18 x^{2}

Rewrite the expression

x^{2} \times x^{2} - x^{2} \times 18

Solution

x^{2} (x^{2} - 18)

Show Solution

x_{1} = - 32, x_{2} = 0, x_{3} = 32

Alternative Form

x_{1} \approx - 4.242641, x_{2} = 0, x_{3} \approx 4.242641

Evaluate

(x^{4} - 18 x^{2})

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

x^{4} - 18 x^{2} = 0

Factor the expression

x^{2} (x^{2} - 18) = 0

Separate the equation into 2 possible cases

x^{2} = 0 x^{2} - 18 = 0

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

x = 0 x^{2} - 18 = 0

Solve the equation

More Steps

Evaluate

x^{2} - 18 = 0

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

x^{2} = 0 + 18

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

x^{2} = 18

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

x = \pm 18

Simplify the expression

More Steps

Evaluate

18

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

9 \times 2

Write the number in exponential form with the base of 3

3^{2} \times 2

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

3^{2} \times 2

Reduce the index of the radical and exponent with 2

32

x = \pm 32

Separate the equation into 2 possible cases

x = 32 x = - 32

x = 0 x = 32 x = - 32

Solution

x_{1} = - 32, x_{2} = 0, x_{3} = 32

Alternative Form

x_{1} \approx - 4.242641, x_{2} = 0, x_{3} \approx 4.242641

Show Solution