Solve ctg^(4)*x^6ctg^(2)x-7=0

Question

Solve the equation

Solve for x

Solve for c

Solve for g

x = \frac{7 7 c ^{5} t ^{5} g}{c t g}

Evaluate

c t g^{4} x^{6} c t g^{2} x - 7 = 0

Multiply

More Steps

Evaluate

c t g^{4} x^{6} c t g^{2} x

Multiply the terms

c^{2} t g^{4} x^{6} t g^{2} x

Multiply the terms

c^{2} t^{2} g^{4} x^{6} g^{2} x

Multiply the terms with the same base by adding their exponents

c^{2} t^{2} g^{4 + 2} x^{6} \times x

Add the numbers

c^{2} t^{2} g^{6} x^{6} \times x

Multiply the terms with the same base by adding their exponents

c^{2} t^{2} g^{6} x^{6 + 1}

Add the numbers

c^{2} t^{2} g^{6} x^{7}

c^{2} t^{2} g^{6} x^{7} - 7 = 0

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

c^{2} t^{2} g^{6} x^{7} = 0 + 7

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

c^{2} t^{2} g^{6} x^{7} = 7

Divide both sides

\frac{c ^{2} t ^{2} g ^{6} x ^{7}}{c ^{2} t ^{2} g ^{6}} = \frac{7}{c ^{2} t ^{2} g ^{6}}

Divide the numbers

x^{7} = \frac{7}{c ^{2} t ^{2} g ^{6}}

Take the 7 -th root on both sides of the equation

7 x^{7} = 7 \frac{7}{c ^{2} t ^{2} g ^{6}}

Calculate

x = 7 \frac{7}{c ^{2} t ^{2} g ^{6}}

Solution

More Steps

Evaluate

7 \frac{7}{c ^{2} t ^{2} g ^{6}}

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

\frac{7 7}{7 c ^{2} t ^{2} g ^{6}}

Multiply by the Conjugate

\frac{7 7 \times 7 c ^{5} t ^{5} g}{7 c ^{2} t ^{2} g ^{6} \times 7 c ^{5} t ^{5} g}

Calculate

\frac{7 7 \times 7 c ^{5} t ^{5} g}{c t g}

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

\frac{7 7 c ^{5} t ^{5} g}{c t g}

x = \frac{7 7 c ^{5} t ^{5} g}{c t g}

Show Solution