Solve m^235i^20150-60

Question

Simplify the expression

- 5250 m^{2} - 60

Evaluate

m^{2} \times 35 i^{2} \times 150 - 60

Evaluate the power

m^{2} \times 35 (- 1) \times 150 - 60

Solution

More Steps

Multiply the terms

m^{2} \times 35 (- 1) \times 150

Any expression multiplied by 1 remains the same

- m^{2} \times 35 \times 150

Multiply the terms

- m^{2} \times 5250

Use the commutative property to reorder the terms

- 5250 m^{2}

- 5250 m^{2} - 60

Show Solution

Factor the expression

- 30 (175 m^{2} + 2)

Evaluate

m^{2} \times 35 i^{2} \times 150 - 60

Evaluate the power

m^{2} \times 35 (- 1) \times 150 - 60

Multiply

More Steps

Multiply the terms

m^{2} \times 35 (- 1) \times 150

Any expression multiplied by 1 remains the same

- m^{2} \times 35 \times 150

Multiply the terms

- m^{2} \times 5250

Use the commutative property to reorder the terms

- 5250 m^{2}

- 5250 m^{2} - 60

Solution

- 30 (175 m^{2} + 2)

Show Solution

Find the roots

m_{1} = - \frac{14}{35} i, m_{2} = \frac{14}{35} i

Alternative Form

m_{1} \approx - 0.106904 i, m_{2} \approx 0.106904 i

Evaluate

m^{2} \times 35 i^{2} \times 150 - 60

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

m^{2} \times 35 i^{2} \times 150 - 60 = 0

Evaluate the power

m^{2} \times 35 (- 1) \times 150 - 60 = 0

Multiply

More Steps

Multiply the terms

m^{2} \times 35 (- 1) \times 150

Any expression multiplied by 1 remains the same

- m^{2} \times 35 \times 150

Multiply the terms

- m^{2} \times 5250

Use the commutative property to reorder the terms

- 5250 m^{2}

- 5250 m^{2} - 60 = 0

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

- 5250 m^{2} = 0 + 60

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

- 5250 m^{2} = 60

Change the signs on both sides of the equation

5250 m^{2} = - 60

Divide both sides

\frac{5250 m ^{2}}{5250} = \frac{- 60}{5250}

Divide the numbers

m^{2} = \frac{- 60}{5250}

Divide the numbers

More Steps

Evaluate

\frac{- 60}{5250}

Cancel out the common factor 30

\frac{- 2}{175}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{2}{175}

m^{2} = - \frac{2}{175}

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

m = \pm - \frac{2}{175}

Simplify the expression

More Steps

Evaluate

- \frac{2}{175}

Evaluate the power

\frac{2}{175} \times - 1

Evaluate the power

\frac{2}{175} \times i

Evaluate the power

More Steps

Evaluate

\frac{2}{175}

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

\frac{2}{175}

Simplify the radical expression

\frac{2}{5 7}

Multiply by the Conjugate

\frac{2 \times 7}{5 7 \times 7}

Multiply the numbers

\frac{14}{5 7 \times 7}

Multiply the numbers

\frac{14}{35}

\frac{14}{35} i

m = \pm \frac{14}{35} i

Separate the equation into 2 possible cases

m = \frac{14}{35} i m = - \frac{14}{35} i

Solution

m_{1} = - \frac{14}{35} i, m_{2} = \frac{14}{35} i

Alternative Form

m_{1} \approx - 0.106904 i, m_{2} \approx 0.106904 i

Show Solution