Solve x^4+64 - ScanMath

Question

Factor the expression

(x^{2} - 4 x + 8) (x^{2} + 4 x + 8)

Evaluate

x^{4} + 64

Calculate

x^{4} + 4 x^{3} + 8 x^{2} - 4 x^{3} - 16 x^{2} - 32 x + 8 x^{2} + 32 x + 64

Rewrite the expression

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

Factor out x^{2} from the expression

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

Factor out - 4 x from the expression

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

Factor out 8 from the expression

x^{2} (x^{2} + 4 x + 8) - 4 x (x^{2} + 4 x + 8) + 8 (x^{2} + 4 x + 8)

Solution

(x^{2} - 4 x + 8) (x^{2} + 4 x + 8)

Show Solution

x_{1} = - 2 - 2 i, x_{2} = 2 + 2 i

Evaluate

x^{4} + 64

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

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 4 - 64

Simplify the expression

More Steps

Evaluate

4 - 64

Rewrite the expression

22 \times (\frac{2}{2} + \frac{2}{2} i)

Apply the distributive property

22 \times \frac{2}{2} + 22 \times \frac{2}{2} i

Multiply the numbers

More Steps

Evaluate

22 \times \frac{2}{2}

Reduce the numbers

2 \times 2

When a square root of an expression is multiplied by itself,the result is that expression

2

2 + 22 \times \frac{2}{2} i

Multiply the numbers

2 + 2 i

x = \pm (2 + 2 i)

Separate the equation into 2 possible cases

x = 2 + 2 i x = - 2 - 2 i

Solution

x_{1} = - 2 - 2 i, x_{2} = 2 + 2 i

Show Solution