Solve (x^2)^2-64 - ScanMath

Question

Simplify the expression

x^{4} - 64

Evaluate

(x^{2})^{2} - 64

Multiply the exponents

x^{2 \times 2} - 64

Solution

x^{4} - 64

Show Solution

(x^{2} - 8) (x^{2} + 8)

Evaluate

(x^{2})^{2} - 64

Evaluate

More Steps

Evaluate

(x^{2})^{2}

Multiply the exponents

x^{2 \times 2}

Multiply the numbers

x^{4}

x^{4} - 64

Rewrite the expression in exponential form

(x^{2})^{2} - 8^{2}

Solution

(x^{2} - 8) (x^{2} + 8)

Show Solution

x_{1} = - 22, x_{2} = 22

Alternative Form

x_{1} \approx - 2.828427, x_{2} \approx 2.828427

Evaluate

(x^{2})^{2} - 64

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

(x^{2})^{2} - 64 = 0

Evaluate the power

More Steps

Evaluate

(x^{2})^{2}

Transform the expression

x^{2 \times 2}

Multiply the numbers

x^{4}

x^{4} - 64 = 0

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

x^{4} = 0 + 64

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

x^{4} = 64

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

x = \pm 464

Simplify the expression

More Steps

Evaluate

464

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

4 16 \times 4

Write the number in exponential form with the base of 2

4 2^{4} \times 4

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

4 2^{4} \times 44

Reduce the index of the radical and exponent with 4

244

Simplify the root

22

x = \pm 22

Separate the equation into 2 possible cases

x = 22 x = - 22

Solution

x_{1} = - 22, x_{2} = 22

Alternative Form

x_{1} \approx - 2.828427, x_{2} \approx 2.828427

Show Solution