Solve 6 6/6 6x^6-6

Question

Simplify the expression

42 x^{6} - 6

Evaluate

6 \frac{6}{6} \times 6 x^{6} - 6

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

6 \frac{6}{6}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{6 \times 6 + 6}{6}

Multiply the terms

\frac{36 + 6}{6}

Add the terms

\frac{42}{6}

\frac{42}{6} \times 6 x^{6} - 6

Solution

More Steps

Multiply the terms

\frac{42}{6} \times 6 x^{6}

Multiply the terms

More Steps

Evaluate

\frac{42}{6} \times 6

Reduce the fraction

42 \times 1

Any expression multiplied by 1 remains the same

42

42 x^{6}

42 x^{6} - 6

Show Solution

Factor the expression

6 (7 x^{6} - 1)

Evaluate

6 \frac{6}{6} \times 6 x^{6} - 6

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

6 \frac{6}{6}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{6 \times 6 + 6}{6}

Multiply the terms

\frac{36 + 6}{6}

Add the terms

\frac{42}{6}

\frac{42}{6} \times 6 x^{6} - 6

Multiply the terms

More Steps

Multiply the terms

\frac{42}{6} \times 6 x^{6}

Multiply the terms

More Steps

Evaluate

\frac{42}{6} \times 6

Reduce the fraction

42 \times 1

Any expression multiplied by 1 remains the same

42

42 x^{6}

42 x^{6} - 6

Solution

6 (7 x^{6} - 1)

Show Solution

Find the roots

x_{1} = - \frac{6 16807}{7}, x_{2} = \frac{6 16807}{7}

Alternative Form

x_{1} \approx - 0.72302, x_{2} \approx 0.72302

Evaluate

6 \frac{6}{6} \times 6 x^{6} - 6

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

6 \frac{6}{6} \times 6 x^{6} - 6 = 0

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

6 \frac{6}{6}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{6 \times 6 + 6}{6}

Multiply the terms

\frac{36 + 6}{6}

Add the terms

\frac{42}{6}

\frac{42}{6} \times 6 x^{6} - 6 = 0

Multiply the terms

More Steps

Multiply the terms

\frac{42}{6} \times 6 x^{6}

Multiply the terms

More Steps

Evaluate

\frac{42}{6} \times 6

Reduce the fraction

42 \times 1

Any expression multiplied by 1 remains the same

42

42 x^{6}

42 x^{6} - 6 = 0

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

42 x^{6} = 0 + 6

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

42 x^{6} = 6

Divide both sides

\frac{42 x ^{6}}{42} = \frac{6}{42}

Divide the numbers

x^{6} = \frac{6}{42}

Cancel out the common factor 6

x^{6} = \frac{1}{7}

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

x = \pm 6 \frac{1}{7}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{7}

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

\frac{6 1}{6 7}

Simplify the radical expression

\frac{1}{6 7}

Multiply by the Conjugate

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

Simplify

\frac{6 16807}{6 7 \times 6 7 ^{5}}

Multiply the numbers

More Steps

Evaluate

67 \times 6 7^{5}

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

6 7 \times 7^{5}

Calculate the product

6 7^{6}

Reduce the index of the radical and exponent with 6

7

\frac{6 16807}{7}

x = \pm \frac{6 16807}{7}

Separate the equation into 2 possible cases

x = \frac{6 16807}{7} x = - \frac{6 16807}{7}

Solution

x_{1} = - \frac{6 16807}{7}, x_{2} = \frac{6 16807}{7}

Alternative Form

x_{1} \approx - 0.72302, x_{2} \approx 0.72302

Show Solution