Solve 2x^3-x^54x^2

Question

Simplify the expression

2 x^{3} - 4 x^{7}

Evaluate

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

Solution

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

x^{5 + 2} \times 4

Add the numbers

x^{7} \times 4

Use the commutative property to reorder the terms

4 x^{7}

2 x^{3} - 4 x^{7}

Show Solution

Factor the expression

2 x^{3} (1 - 2 x^{4})

Evaluate

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

Multiply

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

x^{5 + 2} \times 4

Add the numbers

x^{7} \times 4

Use the commutative property to reorder the terms

4 x^{7}

2 x^{3} - 4 x^{7}

Rewrite the expression

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

Solution

2 x^{3} (1 - 2 x^{4})

Show Solution

Find the roots

x_{1} = - \frac{4 8}{2}, x_{2} = 0, x_{3} = \frac{4 8}{2}

Alternative Form

x_{1} \approx - 0.840896, x_{2} = 0, x_{3} \approx 0.840896

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

x^{5 + 2} \times 4

Add the numbers

x^{7} \times 4

Use the commutative property to reorder the terms

4 x^{7}

2 x^{3} - 4 x^{7} = 0

Factor the expression

2 x^{3} (1 - 2 x^{4}) = 0

Divide both sides

x^{3} (1 - 2 x^{4}) = 0

Separate the equation into 2 possible cases

x^{3} = 0 1 - 2 x^{4} = 0

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

x = 0 1 - 2 x^{4} = 0

Solve the equation

More Steps

Evaluate

1 - 2 x^{4} = 0

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

- 2 x^{4} = 0 - 1

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

- 2 x^{4} = - 1

Change the signs on both sides of the equation

2 x^{4} = 1

Divide both sides

\frac{2 x ^{4}}{2} = \frac{1}{2}

Divide the numbers

x^{4} = \frac{1}{2}

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

x = \pm 4 \frac{1}{2}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{2}

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

\frac{4 1}{4 2}

Simplify the radical expression

\frac{1}{4 2}

Multiply by the Conjugate

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

Simplify

\frac{4 8}{4 2 \times 4 2 ^{3}}

Multiply the numbers

\frac{4 8}{2}

x = \pm \frac{4 8}{2}

Separate the equation into 2 possible cases

x = \frac{4 8}{2} x = - \frac{4 8}{2}

x = 0 x = \frac{4 8}{2} x = - \frac{4 8}{2}

Solution

x_{1} = - \frac{4 8}{2}, x_{2} = 0, x_{3} = \frac{4 8}{2}

Alternative Form

x_{1} \approx - 0.840896, x_{2} = 0, x_{3} \approx 0.840896

Show Solution