Solve 11-128f^2 - ScanMath

Question

Find the roots

f_{1} = - \frac{22}{16}, f_{2} = \frac{22}{16}

Alternative Form

f_{1} \approx - 0.293151, f_{2} \approx 0.293151

Evaluate

11 - 128 f^{2}

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

11 - 128 f^{2} = 0

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

- 128 f^{2} = 0 - 11

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

- 128 f^{2} = - 11

Change the signs on both sides of the equation

128 f^{2} = 11

Divide both sides

\frac{128 f ^{2}}{128} = \frac{11}{128}

Divide the numbers

f^{2} = \frac{11}{128}

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

f = \pm \frac{11}{128}

Simplify the expression

More Steps

Evaluate

\frac{11}{128}

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

\frac{11}{128}

Simplify the radical expression

More Steps

Evaluate

128

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

64 \times 2

Write the number in exponential form with the base of 8

8^{2} \times 2

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

8^{2} \times 2

Reduce the index of the radical and exponent with 2

82

\frac{11}{8 2}

Multiply by the Conjugate

\frac{11 \times 2}{8 2 \times 2}

Multiply the numbers

More Steps

Evaluate

11 \times 2

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

11 \times 2

Calculate the product

22

\frac{22}{8 2 \times 2}

Multiply the numbers

More Steps

Evaluate

82 \times 2

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

8 \times 2

Multiply the terms

16

\frac{22}{16}

f = \pm \frac{22}{16}

Separate the equation into 2 possible cases

f = \frac{22}{16} f = - \frac{22}{16}

Solution

f_{1} = - \frac{22}{16}, f_{2} = \frac{22}{16}

Alternative Form

f_{1} \approx - 0.293151, f_{2} \approx 0.293151

Show Solution