Solve 100-400 f^2

Question

Factor the expression

100 (1 - 2 f) (1 + 2 f)

Evaluate

100 - 400 f^{2}

Factor out 100 from the expression

100 (1 - 4 f^{2})

Solution

More Steps

Evaluate

1 - 4 f^{2}

Rewrite the expression in exponential form

1^{2} - (2 f)^{2}

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(1 - 2 f) (1 + 2 f)

100 (1 - 2 f) (1 + 2 f)

Show Solution

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

Alternative Form

f_{1} = - 0.5, f_{2} = 0.5

Evaluate

100 - 400 f^{2}

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

100 - 400 f^{2} = 0

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

- 400 f^{2} = 0 - 100

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

- 400 f^{2} = - 100

Change the signs on both sides of the equation

400 f^{2} = 100

Divide both sides

\frac{400 f ^{2}}{400} = \frac{100}{400}

Divide the numbers

f^{2} = \frac{100}{400}

Cancel out the common factor 100

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

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

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

Simplify the expression

More Steps

Evaluate

\frac{1}{4}

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

\frac{1}{4}

Simplify the radical expression

\frac{1}{4}

Simplify the radical expression

More Steps

Evaluate

4

Write the number in exponential form with the base of 2

2^{2}

Reduce the index of the radical and exponent with 2

2

\frac{1}{2}

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

Separate the equation into 2 possible cases

f = \frac{1}{2} f = - \frac{1}{2}

Solution

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

Alternative Form

f_{1} = - 0.5, f_{2} = 0.5

Show Solution