Solve 2x^3x^5 = 65

Question

Solve the equation

x_{1} = - \frac{8 8320}{2}, x_{2} = \frac{8 8320}{2}

Alternative Form

x_{1} \approx - 1.545203, x_{2} \approx 1.545203

Evaluate

2 x^{3} \times x^{5} = 65

Multiply

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

2 x^{3 + 5}

Add the numbers

2 x^{8}

2 x^{8} = 65

Divide both sides

\frac{2 x ^{8}}{2} = \frac{65}{2}

Divide the numbers

x^{8} = \frac{65}{2}

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

x = \pm 8 \frac{65}{2}

Simplify the expression

More Steps

Evaluate

8 \frac{65}{2}

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

\frac{8 65}{8 2}

Multiply by the Conjugate

\frac{8 65 \times 8 2 ^{7}}{8 2 \times 8 2 ^{7}}

Simplify

\frac{8 65 \times 8 128}{8 2 \times 8 2 ^{7}}

Multiply the numbers

More Steps

Evaluate

865 \times 8128

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

8 65 \times 128

Calculate the product

88320

\frac{8 8320}{8 2 \times 8 2 ^{7}}

Multiply the numbers

More Steps

Evaluate

82 \times 8 2^{7}

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

8 2 \times 2^{7}

Calculate the product

8 2^{8}

Reduce the index of the radical and exponent with 8

2

\frac{8 8320}{2}

x = \pm \frac{8 8320}{2}

Separate the equation into 2 possible cases

x = \frac{8 8320}{2} x = - \frac{8 8320}{2}

Solution

x_{1} = - \frac{8 8320}{2}, x_{2} = \frac{8 8320}{2}

Alternative Form

x_{1} \approx - 1.545203, x_{2} \approx 1.545203

Show Solution