Solve 7-14 f^4 - ScanMath

Question

Factor the expression

7 (1 - 2 f^{4})

Evaluate

7 - 14 f^{4}

Solution

7 (1 - 2 f^{4})

Show Solution

f_{1} = - \frac{4 8}{2}, f_{2} = \frac{4 8}{2}

Alternative Form

f_{1} \approx - 0.840896, f_{2} \approx 0.840896

Evaluate

7 - 14 f^{4}

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

7 - 14 f^{4} = 0

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

- 14 f^{4} = 0 - 7

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

- 14 f^{4} = - 7

Change the signs on both sides of the equation

14 f^{4} = 7

Divide both sides

\frac{14 f ^{4}}{14} = \frac{7}{14}

Divide the numbers

f^{4} = \frac{7}{14}

Cancel out the common factor 7

f^{4} = \frac{1}{2}

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

f = \pm 4 \frac{1}{2}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{2}

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

\frac{4 1}{4 2}

Simplify the radical expression

\frac{1}{4 2}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

More Steps

Evaluate

42 \times 4 2^{3}

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

4 2 \times 2^{3}

Calculate the product

4 2^{4}

Reduce the index of the radical and exponent with 4

2

\frac{4 8}{2}

f = \pm \frac{4 8}{2}

Separate the equation into 2 possible cases

f = \frac{4 8}{2} f = - \frac{4 8}{2}

Solution

f_{1} = - \frac{4 8}{2}, f_{2} = \frac{4 8}{2}

Alternative Form

f_{1} \approx - 0.840896, f_{2} \approx 0.840896

Show Solution