Solve -5x(-2x^(2)-5)

Question

Simplify the expression

10 x^{3} + 25 x

Evaluate

- 5 x (- 2 x^{2} - 5)

Apply the distributive property

- 5 x (- 2 x^{2}) - (- 5 x \times 5)

Multiply the terms

More Steps

Evaluate

- 5 x (- 2 x^{2})

Multiply the numbers

More Steps

Evaluate

- 5 (- 2)

Multiplying or dividing an even number of negative terms equals a positive

5 \times 2

Multiply the numbers

10

10 x \times x^{2}

Multiply the terms

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Evaluate

x \times x^{2}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{1 + 2}

Add the numbers

x^{3}

10 x^{3}

10 x^{3} - (- 5 x \times 5)

Multiply the numbers

10 x^{3} - (- 25 x)

Solution

10 x^{3} + 25 x

Show Solution

x_{1} = - \frac{10}{2} i, x_{2} = \frac{10}{2} i, x_{3} = 0

Alternative Form

x_{1} \approx - 1.581139 i, x_{2} \approx 1.581139 i, x_{3} = 0

Evaluate

- 5 x (- 2 x^{2} - 5)

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

- 5 x (- 2 x^{2} - 5) = 0

Change the sign

5 x (- 2 x^{2} - 5) = 0

Elimination the left coefficient

x (- 2 x^{2} - 5) = 0

Separate the equation into 2 possible cases

x = 0 - 2 x^{2} - 5 = 0

Solve the equation

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Evaluate

- 2 x^{2} - 5 = 0

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

- 2 x^{2} = 0 + 5

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

- 2 x^{2} = 5

Change the signs on both sides of the equation

2 x^{2} = - 5

Divide both sides

\frac{2 x ^{2}}{2} = \frac{- 5}{2}

Divide the numbers

x^{2} = \frac{- 5}{2}

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

x^{2} = - \frac{5}{2}

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

x = \pm - \frac{5}{2}

Simplify the expression

More Steps

Evaluate

- \frac{5}{2}

Evaluate the power

\frac{5}{2} \times - 1

Evaluate the power

\frac{5}{2} \times i

Evaluate the power

\frac{10}{2} i

x = \pm \frac{10}{2} i

Separate the equation into 2 possible cases

x = \frac{10}{2} i x = - \frac{10}{2} i

x = 0 x = \frac{10}{2} i x = - \frac{10}{2} i

Solution

x_{1} = - \frac{10}{2} i, x_{2} = \frac{10}{2} i, x_{3} = 0

Alternative Form

x_{1} \approx - 1.581139 i, x_{2} \approx 1.581139 i, x_{3} = 0

Show Solution