Solve 3x^5*2x - 7

Question

Simplify the expression

6 x^{6} - 7

Evaluate

3 x^{5} \times 2 x - 7

Solution

More Steps

Evaluate

3 x^{5} \times 2 x

Multiply the terms

6 x^{5} \times x

Multiply the terms with the same base by adding their exponents

6 x^{5 + 1}

Add the numbers

6 x^{6}

6 x^{6} - 7

Show Solution

x_{1} = - \frac{6 54432}{6}, x_{2} = \frac{6 54432}{6}

Alternative Form

x_{1} \approx - 1.026025, x_{2} \approx 1.026025

Evaluate

3 x^{5} \times 2 x - 7

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

3 x^{5} \times 2 x - 7 = 0

Multiply

More Steps

Multiply the terms

3 x^{5} \times 2 x

Multiply the terms

6 x^{5} \times x

Multiply the terms with the same base by adding their exponents

6 x^{5 + 1}

Add the numbers

6 x^{6}

6 x^{6} - 7 = 0

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

6 x^{6} = 0 + 7

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

6 x^{6} = 7

Divide both sides

\frac{6 x ^{6}}{6} = \frac{7}{6}

Divide the numbers

x^{6} = \frac{7}{6}

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

x = \pm 6 \frac{7}{6}

Simplify the expression

More Steps

Evaluate

6 \frac{7}{6}

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

\frac{6 7}{6 6}

Multiply by the Conjugate

\frac{6 7 \times 6 6 ^{5}}{6 6 \times 6 6 ^{5}}

Simplify

\frac{6 7 \times 6 7776}{6 6 \times 6 6 ^{5}}

Multiply the numbers

More Steps

Evaluate

67 \times 67776

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

6 7 \times 7776

Calculate the product

654432

\frac{6 54432}{6 6 \times 6 6 ^{5}}

Multiply the numbers

More Steps

Evaluate

66 \times 6 6^{5}

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

6 6 \times 6^{5}

Calculate the product

6 6^{6}

Reduce the index of the radical and exponent with 6

6

\frac{6 54432}{6}

x = \pm \frac{6 54432}{6}

Separate the equation into 2 possible cases

x = \frac{6 54432}{6} x = - \frac{6 54432}{6}

Solution

x_{1} = - \frac{6 54432}{6}, x_{2} = \frac{6 54432}{6}

Alternative Form

x_{1} \approx - 1.026025, x_{2} \approx 1.026025

Show Solution