Solve 24-70 f^2 - ScanMath

Question

Factor the expression

2 (12 - 35 f^{2})

Evaluate

24 - 70 f^{2}

Solution

2 (12 - 35 f^{2})

Show Solution

f_{1} = - \frac{2 105}{35}, f_{2} = \frac{2 105}{35}

Alternative Form

f_{1} \approx - 0.58554, f_{2} \approx 0.58554

Evaluate

24 - 70 f^{2}

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

24 - 70 f^{2} = 0

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

- 70 f^{2} = 0 - 24

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

- 70 f^{2} = - 24

Change the signs on both sides of the equation

70 f^{2} = 24

Divide both sides

\frac{70 f ^{2}}{70} = \frac{24}{70}

Divide the numbers

f^{2} = \frac{24}{70}

Cancel out the common factor 2

f^{2} = \frac{12}{35}

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

f = \pm \frac{12}{35}

Simplify the expression

More Steps

Evaluate

\frac{12}{35}

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

\frac{12}{35}

Simplify the radical expression

More Steps

Evaluate

12

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

4 \times 3

Write the number in exponential form with the base of 2

2^{2} \times 3

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

2^{2} \times 3

Reduce the index of the radical and exponent with 2

23

\frac{2 3}{35}

Multiply by the Conjugate

\frac{2 3 \times 35}{35 \times 35}

Multiply the numbers

More Steps

Evaluate

3 \times 35

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

3 \times 35

Calculate the product

105

\frac{2 105}{35 \times 35}

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

\frac{2 105}{35}

f = \pm \frac{2 105}{35}

Separate the equation into 2 possible cases

f = \frac{2 105}{35} f = - \frac{2 105}{35}

Solution

f_{1} = - \frac{2 105}{35}, f_{2} = \frac{2 105}{35}

Alternative Form

f_{1} \approx - 0.58554, f_{2} \approx 0.58554

Show Solution