Solve (x^4-6x^2 8)

Question

Simplify the expression

x^{4} - 48 x^{2}

Evaluate

x^{4} - 6 x^{2} \times 8

Solution

x^{4} - 48 x^{2}

Show Solution

x^{2} (x^{2} - 48)

Evaluate

x^{4} - 6 x^{2} \times 8

Multiply the terms

x^{4} - 48 x^{2}

Rewrite the expression

x^{2} \times x^{2} - x^{2} \times 48

Solution

x^{2} (x^{2} - 48)

Show Solution

x_{1} = - 43, x_{2} = 0, x_{3} = 43

Alternative Form

x_{1} \approx - 6.928203, x_{2} = 0, x_{3} \approx 6.928203

Evaluate

(x^{4} - 6 x^{2} \times 8)

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

x^{4} - 6 x^{2} \times 8 = 0

Multiply the terms

x^{4} - 48 x^{2} = 0

Factor the expression

x^{2} (x^{2} - 48) = 0

Separate the equation into 2 possible cases

x^{2} = 0 x^{2} - 48 = 0

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

x = 0 x^{2} - 48 = 0

Solve the equation

More Steps

Evaluate

x^{2} - 48 = 0

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

x^{2} = 0 + 48

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

x^{2} = 48

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

x = \pm 48

Simplify the expression

More Steps

Evaluate

48

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

16 \times 3

Write the number in exponential form with the base of 4

4^{2} \times 3

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

4^{2} \times 3

Reduce the index of the radical and exponent with 2

43

x = \pm 43

Separate the equation into 2 possible cases

x = 43 x = - 43

x = 0 x = 43 x = - 43

Solution

x_{1} = - 43, x_{2} = 0, x_{3} = 43

Alternative Form

x_{1} \approx - 6.928203, x_{2} = 0, x_{3} \approx 6.928203

Show Solution