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

Question

Simplify the expression

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

Evaluate

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

Solution

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

2 x^{3 + 2}

Add the numbers

2 x^{5}

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

Show Solution

Factor the expression

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

Evaluate

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

Multiply

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

2 x^{3 + 2}

Add the numbers

2 x^{5}

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

Rewrite the expression

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

Solution

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

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 20}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 1.357209

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

2 x^{3 + 2}

Add the numbers

2 x^{5}

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

Factor the expression

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

Separate the equation into 2 possible cases

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

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

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

Solve the equation

More Steps

Evaluate

2 x^{3} - 5 = 0

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

2 x^{3} = 0 + 5

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

2 x^{3} = 5

Divide both sides

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

Divide the numbers

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

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

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

Calculate

x = 3 \frac{5}{2}

Simplify the root

More Steps

Evaluate

3 \frac{5}{2}

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

\frac{3 5}{3 2}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

\frac{3 20}{3 2 \times 3 2 ^{2}}

Multiply the numbers

\frac{3 20}{2}

x = \frac{3 20}{2}

x = 0 x = \frac{3 20}{2}

Solution

x_{1} = 0, x_{2} = \frac{3 20}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 1.357209

Show Solution