Solve 24-105 f^4 - ScanMath

Question

Factor the expression

3 (8 - 35 f^{4})

Evaluate

24 - 105 f^{4}

Solution

3 (8 - 35 f^{4})

Show Solution

f_{1} = - \frac{4 343000}{35}, f_{2} = \frac{4 343000}{35}

Alternative Form

f_{1} \approx - 0.691442, f_{2} \approx 0.691442

Evaluate

24 - 105 f^{4}

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

24 - 105 f^{4} = 0

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

- 105 f^{4} = 0 - 24

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

- 105 f^{4} = - 24

Change the signs on both sides of the equation

105 f^{4} = 24

Divide both sides

\frac{105 f ^{4}}{105} = \frac{24}{105}

Divide the numbers

f^{4} = \frac{24}{105}

Cancel out the common factor 3

f^{4} = \frac{8}{35}

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

f = \pm 4 \frac{8}{35}

Simplify the expression

More Steps

Evaluate

4 \frac{8}{35}

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

\frac{4 8}{4 35}

Multiply by the Conjugate

\frac{4 8 \times 4 3 5 ^{3}}{4 35 \times 4 3 5 ^{3}}

Simplify

\frac{4 8 \times 4 42875}{4 35 \times 4 3 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

48 \times 442875

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

4 8 \times 42875

Calculate the product

4343000

\frac{4 343000}{4 35 \times 4 3 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

435 \times 4 3 5^{3}

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

4 35 \times 3 5^{3}

Calculate the product

4 3 5^{4}

Reduce the index of the radical and exponent with 4

35

\frac{4 343000}{35}

f = \pm \frac{4 343000}{35}

Separate the equation into 2 possible cases

f = \frac{4 343000}{35} f = - \frac{4 343000}{35}

Solution

f_{1} = - \frac{4 343000}{35}, f_{2} = \frac{4 343000}{35}

Alternative Form

f_{1} \approx - 0.691442, f_{2} \approx 0.691442

Show Solution