Solve 20-70 f^2 - ScanMath

Question

Factor the expression

10 (2 - 7 f^{2})

Evaluate

20 - 70 f^{2}

Solution

10 (2 - 7 f^{2})

Show Solution

f_{1} = - \frac{14}{7}, f_{2} = \frac{14}{7}

Alternative Form

f_{1} \approx - 0.534522, f_{2} \approx 0.534522

Evaluate

20 - 70 f^{2}

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

20 - 70 f^{2} = 0

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

- 70 f^{2} = 0 - 20

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

- 70 f^{2} = - 20

Change the signs on both sides of the equation

70 f^{2} = 20

Divide both sides

\frac{70 f ^{2}}{70} = \frac{20}{70}

Divide the numbers

f^{2} = \frac{20}{70}

Cancel out the common factor 10

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

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

f = \pm \frac{2}{7}

Simplify the expression

More Steps

Evaluate

\frac{2}{7}

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

\frac{2}{7}

Multiply by the Conjugate

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

Multiply the numbers

More Steps

Evaluate

2 \times 7

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

2 \times 7

Calculate the product

14

\frac{14}{7 \times 7}

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

\frac{14}{7}

f = \pm \frac{14}{7}

Separate the equation into 2 possible cases

f = \frac{14}{7} f = - \frac{14}{7}

Solution

f_{1} = - \frac{14}{7}, f_{2} = \frac{14}{7}

Alternative Form

f_{1} \approx - 0.534522, f_{2} \approx 0.534522

Show Solution