Solve 15-35 f^2 - ScanMath

Question

Factor the expression

5 (3 - 7 f^{2})

Evaluate

15 - 35 f^{2}

Solution

5 (3 - 7 f^{2})

Show Solution

f_{1} = - \frac{21}{7}, f_{2} = \frac{21}{7}

Alternative Form

f_{1} \approx - 0.654654, f_{2} \approx 0.654654

Evaluate

15 - 35 f^{2}

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

15 - 35 f^{2} = 0

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

- 35 f^{2} = 0 - 15

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

- 35 f^{2} = - 15

Change the signs on both sides of the equation

35 f^{2} = 15

Divide both sides

\frac{35 f ^{2}}{35} = \frac{15}{35}

Divide the numbers

f^{2} = \frac{15}{35}

Cancel out the common factor 5

f^{2} = \frac{3}{7}

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

f = \pm \frac{3}{7}

Simplify the expression

More Steps

Evaluate

\frac{3}{7}

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

\frac{3}{7}

Multiply by the Conjugate

\frac{3 \times 7}{7 \times 7}

Multiply the numbers

More Steps

Evaluate

3 \times 7

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

3 \times 7

Calculate the product

21

\frac{21}{7 \times 7}

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

\frac{21}{7}

f = \pm \frac{21}{7}

Separate the equation into 2 possible cases

f = \frac{21}{7} f = - \frac{21}{7}

Solution

f_{1} = - \frac{21}{7}, f_{2} = \frac{21}{7}

Alternative Form

f_{1} \approx - 0.654654, f_{2} \approx 0.654654

Show Solution