Solve 70-200 f^28

Question

Simplify the expression

70 - 1600 f^{2}

Evaluate

70 - 200 f^{2} \times 8

Solution

70 - 1600 f^{2}

Show Solution

10 (7 - 160 f^{2})

Evaluate

70 - 200 f^{2} \times 8

Multiply the terms

70 - 1600 f^{2}

Solution

10 (7 - 160 f^{2})

Show Solution

f_{1} = - \frac{70}{40}, f_{2} = \frac{70}{40}

Alternative Form

f_{1} \approx - 0.209165, f_{2} \approx 0.209165

Evaluate

70 - 200 f^{2} \times 8

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

70 - 200 f^{2} \times 8 = 0

Multiply the terms

70 - 1600 f^{2} = 0

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

- 1600 f^{2} = 0 - 70

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

- 1600 f^{2} = - 70

Change the signs on both sides of the equation

1600 f^{2} = 70

Divide both sides

\frac{1600 f ^{2}}{1600} = \frac{70}{1600}

Divide the numbers

f^{2} = \frac{70}{1600}

Cancel out the common factor 10

f^{2} = \frac{7}{160}

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

f = \pm \frac{7}{160}

Simplify the expression

More Steps

Evaluate

\frac{7}{160}

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

\frac{7}{160}

Simplify the radical expression

More Steps

Evaluate

160

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

16 \times 10

Write the number in exponential form with the base of 4

4^{2} \times 10

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

4^{2} \times 10

Reduce the index of the radical and exponent with 2

410

\frac{7}{4 10}

Multiply by the Conjugate

\frac{7 \times 10}{4 10 \times 10}

Multiply the numbers

More Steps

Evaluate

7 \times 10

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

7 \times 10

Calculate the product

70

\frac{70}{4 10 \times 10}

Multiply the numbers

More Steps

Evaluate

410 \times 10

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

4 \times 10

Multiply the terms

40

\frac{70}{40}

f = \pm \frac{70}{40}

Separate the equation into 2 possible cases

f = \frac{70}{40} f = - \frac{70}{40}

Solution

f_{1} = - \frac{70}{40}, f_{2} = \frac{70}{40}

Alternative Form

f_{1} \approx - 0.209165, f_{2} \approx 0.209165

Show Solution