Solve x^3-2x^2/5x^3

Question

Simplify the expression

\frac{5 x ^{3} - 2 x ^{5}}{5}

Evaluate

x^{3} - (2 \times \frac{x ^{2}}{5}) x^{3}

Remove the parentheses

x^{3} - 2 \times \frac{x ^{2}}{5} x^{3}

Multiply the terms

More Steps

Multiply the terms

2 \times \frac{x ^{2}}{5} x^{3}

Multiply the terms

\frac{2 x ^{2}}{5} x^{3}

Multiply the terms

\frac{2 x ^{2} \times x ^{3}}{5}

Multiply the terms

More Steps

Evaluate

x^{2} \times x^{3}

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

x^{2 + 3}

Add the numbers

x^{5}

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

x^{3} - \frac{2 x ^{5}}{5}

Reduce fractions to a common denominator

\frac{x ^{3} \times 5}{5} - \frac{2 x ^{5}}{5}

Write all numerators above the common denominator

\frac{x ^{3} \times 5 - 2 x ^{5}}{5}

Solution

\frac{5 x ^{3} - 2 x ^{5}}{5}

Show Solution

Find the roots

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

Alternative Form

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

Evaluate

x^{3} - (2 \times \frac{x ^{2}}{5}) x^{3}

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

x^{3} - (2 \times \frac{x ^{2}}{5}) x^{3} = 0

Multiply the terms

x^{3} - \frac{2 x ^{2}}{5} x^{3} = 0

Multiply the terms

More Steps

Multiply the terms

\frac{2 x ^{2}}{5} x^{3}

Multiply the terms

\frac{2 x ^{2} \times x ^{3}}{5}

Multiply the terms

More Steps

Evaluate

x^{2} \times x^{3}

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

x^{2 + 3}

Add the numbers

x^{5}

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

x^{3} - \frac{2 x ^{5}}{5} = 0

Subtract the terms

More Steps

Simplify

x^{3} - \frac{2 x ^{5}}{5}

Reduce fractions to a common denominator

\frac{x ^{3} \times 5}{5} - \frac{2 x ^{5}}{5}

Write all numerators above the common denominator

\frac{x ^{3} \times 5 - 2 x ^{5}}{5}

Use the commutative property to reorder the terms

\frac{5 x ^{3} - 2 x ^{5}}{5}

\frac{5 x ^{3} - 2 x ^{5}}{5} = 0

Simplify

5 x^{3} - 2 x^{5} = 0

Factor the expression

x^{3} (5 - 2 x^{2}) = 0

Separate the equation into 2 possible cases

x^{3} = 0 5 - 2 x^{2} = 0

The only way a power can be 0 is when the base equals 0

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

Solve the equation

More Steps

Evaluate

5 - 2 x^{2} = 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}

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}

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

\frac{5}{2}

Multiply by the Conjugate

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

Multiply the numbers

\frac{10}{2 \times 2}

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

\frac{10}{2}

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

Separate the equation into 2 possible cases

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

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

Solution

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

Alternative Form

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

Show Solution