Solve 2x^4 x^3 - x^2

Question

Simplify the expression

2 x^{7} - x^{2}

Evaluate

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

Solution

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

2 x^{4 + 3}

Add the numbers

2 x^{7}

2 x^{7} - x^{2}

Show Solution

Factor the expression

x^{2} (2 x^{5} - 1)

Evaluate

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

Multiply

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

2 x^{4 + 3}

Add the numbers

2 x^{7}

2 x^{7} - x^{2}

Rewrite the expression

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

Solution

x^{2} (2 x^{5} - 1)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{5 16}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 0.870551

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

2 x^{4 + 3}

Add the numbers

2 x^{7}

2 x^{7} - x^{2} = 0

Factor the expression

x^{2} (2 x^{5} - 1) = 0

Separate the equation into 2 possible cases

x^{2} = 0 2 x^{5} - 1 = 0

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

x = 0 2 x^{5} - 1 = 0

Solve the equation

More Steps

Evaluate

2 x^{5} - 1 = 0

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

2 x^{5} = 0 + 1

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

2 x^{5} = 1

Divide both sides

\frac{2 x ^{5}}{2} = \frac{1}{2}

Divide the numbers

x^{5} = \frac{1}{2}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{1}{2}

Calculate

x = 5 \frac{1}{2}

Simplify the root

More Steps

Evaluate

5 \frac{1}{2}

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

\frac{5 1}{5 2}

Simplify the radical expression

\frac{1}{5 2}

Multiply by the Conjugate

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

Simplify

\frac{5 16}{5 2 \times 5 2 ^{4}}

Multiply the numbers

\frac{5 16}{2}

x = \frac{5 16}{2}

x = 0 x = \frac{5 16}{2}

Solution

x_{1} = 0, x_{2} = \frac{5 16}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 0.870551

Show Solution