Solve 12-45 f^4 - ScanMath

Question

Factor the expression

3 (4 - 15 f^{4})

Evaluate

12 - 45 f^{4}

Solution

3 (4 - 15 f^{4})

Show Solution

f_{1} = - \frac{4 13500}{15}, f_{2} = \frac{4 13500}{15}

Alternative Form

f_{1} \approx - 0.718608, f_{2} \approx 0.718608

Evaluate

12 - 45 f^{4}

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

12 - 45 f^{4} = 0

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

- 45 f^{4} = 0 - 12

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

- 45 f^{4} = - 12

Change the signs on both sides of the equation

45 f^{4} = 12

Divide both sides

\frac{45 f ^{4}}{45} = \frac{12}{45}

Divide the numbers

f^{4} = \frac{12}{45}

Cancel out the common factor 3

f^{4} = \frac{4}{15}

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

f = \pm 4 \frac{4}{15}

Simplify the expression

More Steps

Evaluate

4 \frac{4}{15}

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

\frac{4 4}{4 15}

Simplify the radical expression

More Steps

Evaluate

44

Write the number in exponential form with the base of 2

4 2^{2}

Reduce the index of the radical and exponent with 2

2

\frac{2}{4 15}

Multiply by the Conjugate

\frac{2 \times 4 1 5 ^{3}}{4 15 \times 4 1 5 ^{3}}

Simplify

\frac{2 \times 4 3375}{4 15 \times 4 1 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

2 \times 43375

Use n a = mn a^{m} to expand the expression

4 2^{2} \times 43375

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

4 2^{2} \times 3375

Calculate the product

413500

\frac{4 13500}{4 15 \times 4 1 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

415 \times 4 1 5^{3}

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

4 15 \times 1 5^{3}

Calculate the product

4 1 5^{4}

Reduce the index of the radical and exponent with 4

15

\frac{4 13500}{15}

f = \pm \frac{4 13500}{15}

Separate the equation into 2 possible cases

f = \frac{4 13500}{15} f = - \frac{4 13500}{15}

Solution

f_{1} = - \frac{4 13500}{15}, f_{2} = \frac{4 13500}{15}

Alternative Form

f_{1} \approx - 0.718608, f_{2} \approx 0.718608

Show Solution