Solve -4x^2-5(x^3)*x^2

Question

Simplify the expression

- 4 x^{2} - 5 x^{5}

Evaluate

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

Solution

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

5 x^{3 + 2}

Add the numbers

5 x^{5}

- 4 x^{2} - 5 x^{5}

Show Solution

Factor the expression

- x^{2} (4 + 5 x^{3})

Evaluate

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

Multiply

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

5 x^{3 + 2}

Add the numbers

5 x^{5}

- 4 x^{2} - 5 x^{5}

Rewrite the expression

- x^{2} \times 4 - x^{2} \times 5 x^{3}

Solution

- x^{2} (4 + 5 x^{3})

Show Solution

Find the roots

x_{1} = - \frac{3 100}{5}, x_{2} = 0

Alternative Form

x_{1} \approx - 0.928318, x_{2} = 0

Evaluate

- 4 x^{2} - 5 (x^{3}) x^{2}

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

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

Calculate

- 4 x^{2} - 5 x^{3} \times x^{2} = 0

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

5 x^{3 + 2}

Add the numbers

5 x^{5}

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

Factor the expression

- x^{2} (4 + 5 x^{3}) = 0

Divide both sides

x^{2} (4 + 5 x^{3}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 4 + 5 x^{3} = 0

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

x = 0 4 + 5 x^{3} = 0

Solve the equation

More Steps

Evaluate

4 + 5 x^{3} = 0

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

5 x^{3} = 0 - 4

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

5 x^{3} = - 4

Divide both sides

\frac{5 x ^{3}}{5} = \frac{- 4}{5}

Divide the numbers

x^{3} = \frac{- 4}{5}

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

x^{3} = - \frac{4}{5}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 - \frac{4}{5}

Calculate

x = 3 - \frac{4}{5}

Simplify the root

More Steps

Evaluate

3 - \frac{4}{5}

An odd root of a negative radicand is always a negative

- 3 \frac{4}{5}

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

- \frac{3 4}{3 5}

Multiply by the Conjugate

\frac{- 3 4 \times 3 5 ^{2}}{3 5 \times 3 5 ^{2}}

Simplify

\frac{- 3 4 \times 3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

\frac{- 3 100}{3 5 \times 3 5 ^{2}}

Multiply the numbers

\frac{- 3 100}{5}

Calculate

- \frac{3 100}{5}

x = - \frac{3 100}{5}

x = 0 x = - \frac{3 100}{5}

Solution

x_{1} = - \frac{3 100}{5}, x_{2} = 0

Alternative Form

x_{1} \approx - 0.928318, x_{2} = 0

Show Solution