Solve 28-200f^2 - ScanMath

Question

Factor the expression

4 (7 - 50 f^{2})

Evaluate

28 - 200 f^{2}

Solution

4 (7 - 50 f^{2})

Show Solution

f_{1} = - \frac{14}{10}, f_{2} = \frac{14}{10}

Alternative Form

f_{1} \approx - 0.374166, f_{2} \approx 0.374166

Evaluate

28 - 200 f^{2}

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

28 - 200 f^{2} = 0

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

- 200 f^{2} = 0 - 28

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

- 200 f^{2} = - 28

Change the signs on both sides of the equation

200 f^{2} = 28

Divide both sides

\frac{200 f ^{2}}{200} = \frac{28}{200}

Divide the numbers

f^{2} = \frac{28}{200}

Cancel out the common factor 4

f^{2} = \frac{7}{50}

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

f = \pm \frac{7}{50}

Simplify the expression

More Steps

Evaluate

\frac{7}{50}

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

\frac{7}{50}

Simplify the radical expression

More Steps

Evaluate

50

Write the expression as a product where the root of one of the factors can be evaluated

25 \times 2

Write the number in exponential form with the base of 5

5^{2} \times 2

The root of a product is equal to the product of the roots of each factor

5^{2} \times 2

Reduce the index of the radical and exponent with 2

52

\frac{7}{5 2}

Multiply by the Conjugate

\frac{7 \times 2}{5 2 \times 2}

Multiply the numbers

More Steps

Evaluate

7 \times 2

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

7 \times 2

Calculate the product

14

\frac{14}{5 2 \times 2}

Multiply the numbers

More Steps

Evaluate

52 \times 2

When a square root of an expression is multiplied by itself,the result is that expression

5 \times 2

Multiply the terms

10

\frac{14}{10}

f = \pm \frac{14}{10}

Separate the equation into 2 possible cases

f = \frac{14}{10} f = - \frac{14}{10}

Solution

f_{1} = - \frac{14}{10}, f_{2} = \frac{14}{10}

Alternative Form

f_{1} \approx - 0.374166, f_{2} \approx 0.374166

Show Solution