Solve 6544:2-256x^4

Question

Simplify the expression

3272 - 256 x^{4}

Evaluate

6544 \div 2 - 256 x^{4}

Solution

3272 - 256 x^{4}

Show Solution

8 (409 - 32 x^{4})

Evaluate

6544 \div 2 - 256 x^{4}

Divide the numbers

3272 - 256 x^{4}

Solution

8 (409 - 32 x^{4})

Show Solution

x_{1} = - \frac{4 3272}{4}, x_{2} = \frac{4 3272}{4}

Alternative Form

x_{1} \approx - 1.89079, x_{2} \approx 1.89079

Evaluate

6544 \div 2 - 256 x^{4}

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

6544 \div 2 - 256 x^{4} = 0

Divide the numbers

3272 - 256 x^{4} = 0

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

- 256 x^{4} = 0 - 3272

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

- 256 x^{4} = - 3272

Change the signs on both sides of the equation

256 x^{4} = 3272

Divide both sides

\frac{256 x ^{4}}{256} = \frac{3272}{256}

Divide the numbers

x^{4} = \frac{3272}{256}

Cancel out the common factor 8

x^{4} = \frac{409}{32}

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

x = \pm 4 \frac{409}{32}

Simplify the expression

More Steps

Evaluate

4 \frac{409}{32}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{4 409}{4 32}

Simplify the radical expression

More Steps

Evaluate

432

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

4 16 \times 2

Write the number in exponential form with the base of 2

4 2^{4} \times 2

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

4 2^{4} \times 42

Reduce the index of the radical and exponent with 4

242

\frac{4 409}{2 4 2}

Multiply by the Conjugate

\frac{4 409 \times 4 2 ^{3}}{2 4 2 \times 4 2 ^{3}}

Simplify

\frac{4 409 \times 4 8}{2 4 2 \times 4 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

4409 \times 48

The product of roots with the same index is equal to the root of the product

4 409 \times 8

Calculate the product

43272

\frac{4 3272}{2 4 2 \times 4 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

242 \times 4 2^{3}

Multiply the terms

2 \times 2

Multiply the numbers

4

\frac{4 3272}{4}

x = \pm \frac{4 3272}{4}

Separate the equation into 2 possible cases

x = \frac{4 3272}{4} x = - \frac{4 3272}{4}

Solution

x_{1} = - \frac{4 3272}{4}, x_{2} = \frac{4 3272}{4}

Alternative Form

x_{1} \approx - 1.89079, x_{2} \approx 1.89079

Show Solution