Solve -2r^3 5/10r -3

问题

Simplify the expression

Solution

- r^{4} - 3

Evaluate

- 2 r^{3} \times \frac{5}{10} r - 3

Cancel out the common factor 5

- 2 r^{3} \times \frac{1}{2} r - 3

解题方案

更多步骤

Multiply the terms

- 2 r^{3} \times \frac{1}{2} r

Multiply the terms

更多步骤

Evaluate

2 \times \frac{1}{2}

Reduce the fraction

1 \times 1

Any expression multiplied by 1 remains the same

1

- r^{3} \times r

Multiply the terms with the same base by adding their exponents

- r^{3 + 1}

Add the numbers

- r^{4}

- r^{4} - 3

显示解题方案

Find the roots

Find the roots of the algebra expression

r_{1} = - \frac{4 12}{2} - \frac{4 12}{2} i, r_{2} = \frac{4 12}{2} + \frac{4 12}{2} i

Alternative Form

r_{1} \approx - 0.930605 - 0.930605 i, r_{2} \approx 0.930605 + 0.930605 i

Evaluate

- 2 r^{3} \times \frac{5}{10} r - 3

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

- 2 r^{3} \times \frac{5}{10} r - 3 = 0

Cancel out the common factor 5

- 2 r^{3} \times \frac{1}{2} r - 3 = 0

Multiply

更多步骤

Multiply the terms

- 2 r^{3} \times \frac{1}{2} r

Multiply the terms

更多步骤

Evaluate

2 \times \frac{1}{2}

Reduce the fraction

1 \times 1

Any expression multiplied by 1 remains the same

1

- r^{3} \times r

Multiply the terms with the same base by adding their exponents

- r^{3 + 1}

Add the numbers

- r^{4}

- r^{4} - 3 = 0

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

- r^{4} = 0 + 3

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

- r^{4} = 3

Change the signs on both sides of the equation

r^{4} = - 3

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

r = \pm 4 - 3

Simplify the expression

更多步骤

Evaluate

4 - 3

Rewrite the expression

43 \times (\frac{2}{2} + \frac{2}{2} i)

Apply the distributive property

43 \times \frac{2}{2} + 43 \times \frac{2}{2} i

Multiply the numbers

更多步骤

Evaluate

43 \times \frac{2}{2}

Multiply the numbers

\frac{4 3 \times 2}{2}

Multiply the numbers

\frac{4 12}{2}

\frac{4 12}{2} + 43 \times \frac{2}{2} i

Multiply the numbers

\frac{4 12}{2} + \frac{4 12}{2} i

r = \pm (\frac{4 12}{2} + \frac{4 12}{2} i)

Separate the equation into 2 possible cases

r = \frac{4 12}{2} + \frac{4 12}{2} i r = - \frac{4 12}{2} - \frac{4 12}{2} i

解题方案

r_{1} = - \frac{4 12}{2} - \frac{4 12}{2} i, r_{2} = \frac{4 12}{2} + \frac{4 12}{2} i

Alternative Form

r_{1} \approx - 0.930605 - 0.930605 i, r_{2} \approx 0.930605 + 0.930605 i

显示解题方案

2r^3 5/10r 3

Simplify the expression

Find the roots