Solve x^3*2 x - 1

Question

Simplify the expression

2 x^{4} - 1

Evaluate

x^{3} \times 2 x - 1

Solution

More Steps

Evaluate

x^{3} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{3 + 1} \times 2

Add the numbers

x^{4} \times 2

Use the commutative property to reorder the terms

2 x^{4}

2 x^{4} - 1

Show Solution

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

Alternative Form

x_{1} \approx - 0.840896, x_{2} \approx 0.840896

Evaluate

x^{3} \times 2 x - 1

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

x^{3} \times 2 x - 1 = 0

Multiply

More Steps

Multiply the terms

x^{3} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{3 + 1} \times 2

Add the numbers

x^{4} \times 2

Use the commutative property to reorder the terms

2 x^{4}

2 x^{4} - 1 = 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

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

More Steps

Evaluate

42 \times 4 2^{3}

The product of roots with the same index is equal to the root of the product

4 2 \times 2^{3}

Calculate the product

4 2^{4}

Reduce the index of the radical and exponent with 4

2

\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}

Solution

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

Alternative Form

x_{1} \approx - 0.840896, x_{2} \approx 0.840896

Show Solution