Solve 66x^6-6 - ScanMath

Question

Factor the expression

6 (11 x^{6} - 1)

Evaluate

66 x^{6} - 6

Solution

6 (11 x^{6} - 1)

Show Solution

x_{1} = - \frac{6 1 1 ^{5}}{11}, x_{2} = \frac{6 1 1 ^{5}}{11}

Alternative Form

x_{1} \approx - 0.670555, x_{2} \approx 0.670555

Evaluate

66 x^{6} - 6

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

66 x^{6} - 6 = 0

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

66 x^{6} = 0 + 6

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

66 x^{6} = 6

Divide both sides

\frac{66 x ^{6}}{66} = \frac{6}{66}

Divide the numbers

x^{6} = \frac{6}{66}

Cancel out the common factor 6

x^{6} = \frac{1}{11}

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

x = \pm 6 \frac{1}{11}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{11}

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

\frac{6 1}{6 11}

Simplify the radical expression

\frac{1}{6 11}

Multiply by the Conjugate

\frac{6 1 1 ^{5}}{6 11 \times 6 1 1 ^{5}}

Multiply the numbers

More Steps

Evaluate

611 \times 6 1 1^{5}

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

6 11 \times 1 1^{5}

Calculate the product

6 1 1^{6}

Reduce the index of the radical and exponent with 6

11

\frac{6 1 1 ^{5}}{11}

x = \pm \frac{6 1 1 ^{5}}{11}

Separate the equation into 2 possible cases

x = \frac{6 1 1 ^{5}}{11} x = - \frac{6 1 1 ^{5}}{11}

Solution

x_{1} = - \frac{6 1 1 ^{5}}{11}, x_{2} = \frac{6 1 1 ^{5}}{11}

Alternative Form

x_{1} \approx - 0.670555, x_{2} \approx 0.670555

Show Solution