Solve 70-200 f^4 - ScanMath

Question

Factor the expression

10 (7 - 20 f^{4})

Evaluate

70 - 200 f^{4}

Solution

10 (7 - 20 f^{4})

Show Solution

f_{1} = - \frac{4 3500}{10}, f_{2} = \frac{4 3500}{10}

Alternative Form

f_{1} \approx - 0.769161, f_{2} \approx 0.769161

Evaluate

70 - 200 f^{4}

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

70 - 200 f^{4} = 0

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

- 200 f^{4} = 0 - 70

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

- 200 f^{4} = - 70

Change the signs on both sides of the equation

200 f^{4} = 70

Divide both sides

\frac{200 f ^{4}}{200} = \frac{70}{200}

Divide the numbers

f^{4} = \frac{70}{200}

Cancel out the common factor 10

f^{4} = \frac{7}{20}

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

f = \pm 4 \frac{7}{20}

Simplify the expression

More Steps

Evaluate

4 \frac{7}{20}

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

\frac{4 7}{4 20}

Multiply by the Conjugate

\frac{4 7 \times 4 2 0 ^{3}}{4 20 \times 4 2 0 ^{3}}

Simplify

\frac{4 7 \times 2 4 500}{4 20 \times 4 2 0 ^{3}}

Multiply the numbers

More Steps

Evaluate

47 \times 24500

Multiply the terms

43500 \times 2

Use the commutative property to reorder the terms

243500

\frac{2 4 3500}{4 20 \times 4 2 0 ^{3}}

Multiply the numbers

More Steps

Evaluate

420 \times 4 2 0^{3}

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

4 20 \times 2 0^{3}

Calculate the product

4 2 0^{4}

Reduce the index of the radical and exponent with 4

20

\frac{2 4 3500}{20}

Cancel out the common factor 2

\frac{4 3500}{10}

f = \pm \frac{4 3500}{10}

Separate the equation into 2 possible cases

f = \frac{4 3500}{10} f = - \frac{4 3500}{10}

Solution

f_{1} = - \frac{4 3500}{10}, f_{2} = \frac{4 3500}{10}

Alternative Form

f_{1} \approx - 0.769161, f_{2} \approx 0.769161

Show Solution