Solve omega^2640-9

Question

Simplify the expression

640 ω^{2} - 9

Evaluate

ω^{2} \times 640 - 9

Solution

640 ω^{2} - 9

Show Solution

ω_{1} = - \frac{3 10}{80}, ω_{2} = \frac{3 10}{80}

Alternative Form

ω_{1} \approx - 0.118585, ω_{2} \approx 0.118585

Evaluate

ω^{2} \times 640 - 9

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

ω^{2} \times 640 - 9 = 0

Use the commutative property to reorder the terms

640 ω^{2} - 9 = 0

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

640 ω^{2} = 0 + 9

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

640 ω^{2} = 9

Divide both sides

\frac{640 ω ^{2}}{640} = \frac{9}{640}

Divide the numbers

ω^{2} = \frac{9}{640}

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

ω = \pm \frac{9}{640}

Simplify the expression

More Steps

Evaluate

\frac{9}{640}

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

\frac{9}{640}

Simplify the radical expression

More Steps

Evaluate

9

Write the number in exponential form with the base of 3

3^{2}

Reduce the index of the radical and exponent with 2

3

\frac{3}{640}

Simplify the radical expression

More Steps

Evaluate

640

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

64 \times 10

Write the number in exponential form with the base of 8

8^{2} \times 10

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

8^{2} \times 10

Reduce the index of the radical and exponent with 2

810

\frac{3}{8 10}

Multiply by the Conjugate

\frac{3 10}{8 10 \times 10}

Multiply the numbers

More Steps

Evaluate

810 \times 10

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

8 \times 10

Multiply the terms

80

\frac{3 10}{80}

ω = \pm \frac{3 10}{80}

Separate the equation into 2 possible cases

ω = \frac{3 10}{80} ω = - \frac{3 10}{80}

Solution

ω_{1} = - \frac{3 10}{80}, ω_{2} = \frac{3 10}{80}

Alternative Form

ω_{1} \approx - 0.118585, ω_{2} \approx 0.118585

Show Solution