Solve 501-6x^6 - ScanMath

Question

Factor the expression

3 (167 - 2 x^{6})

Evaluate

501 - 6 x^{6}

Solution

3 (167 - 2 x^{6})

Show Solution

x_{1} = - \frac{6 5344}{2}, x_{2} = \frac{6 5344}{2}

Alternative Form

x_{1} \approx - 2.090649, x_{2} \approx 2.090649

Evaluate

501 - 6 x^{6}

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

501 - 6 x^{6} = 0

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

- 6 x^{6} = 0 - 501

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

- 6 x^{6} = - 501

Change the signs on both sides of the equation

6 x^{6} = 501

Divide both sides

\frac{6 x ^{6}}{6} = \frac{501}{6}

Divide the numbers

x^{6} = \frac{501}{6}

Cancel out the common factor 3

x^{6} = \frac{167}{2}

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

x = \pm 6 \frac{167}{2}

Simplify the expression

More Steps

Evaluate

6 \frac{167}{2}

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

\frac{6 167}{6 2}

Multiply by the Conjugate

\frac{6 167 \times 6 2 ^{5}}{6 2 \times 6 2 ^{5}}

Simplify

\frac{6 167 \times 6 32}{6 2 \times 6 2 ^{5}}

Multiply the numbers

More Steps

Evaluate

6167 \times 632

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

6 167 \times 32

Calculate the product

65344

\frac{6 5344}{6 2 \times 6 2 ^{5}}

Multiply the numbers

More Steps

Evaluate

62 \times 6 2^{5}

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

6 2 \times 2^{5}

Calculate the product

6 2^{6}

Reduce the index of the radical and exponent with 6

2

\frac{6 5344}{2}

x = \pm \frac{6 5344}{2}

Separate the equation into 2 possible cases

x = \frac{6 5344}{2} x = - \frac{6 5344}{2}

Solution

x_{1} = - \frac{6 5344}{2}, x_{2} = \frac{6 5344}{2}

Alternative Form

x_{1} \approx - 2.090649, x_{2} \approx 2.090649

Show Solution