Solve ctg4x^6ctg2x-7=0

Question

Solve the equation

Solve for x

Solve for c

Solve for g

x = \frac{7 112 c ^{5} t ^{5} g ^{5}}{2 c t g}

Evaluate

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

Multiply

More Steps

Evaluate

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

Multiply the terms

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

Multiply the terms

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

Multiply the terms

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

Multiply the terms

c^{2} t^{2} g^{2} \times 8 x^{6} \times x

Multiply the terms with the same base by adding their exponents

c^{2} t^{2} g^{2} \times 8 x^{6 + 1}

Add the numbers

c^{2} t^{2} g^{2} \times 8 x^{7}

Use the commutative property to reorder the terms

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

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

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

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

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

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

Divide both sides

\frac{8 c ^{2} t ^{2} g ^{2} x ^{7}}{8 c ^{2} t ^{2} g ^{2}} = \frac{7}{8 c ^{2} t ^{2} g ^{2}}

Divide the numbers

x^{7} = \frac{7}{8 c ^{2} t ^{2} g ^{2}}

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

7 x^{7} = 7 \frac{7}{8 c ^{2} t ^{2} g ^{2}}

Calculate

x = 7 \frac{7}{8 c ^{2} t ^{2} g ^{2}}

Simplify the root

More Steps

Evaluate

7 \frac{7}{8 c ^{2} t ^{2} g ^{2}}

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

\frac{7 7}{7 8 c ^{2} t ^{2} g ^{2}}

Multiply by the Conjugate

\frac{7 7 \times 7 8 ^{6} c ^{5} t ^{5} g ^{5}}{7 8 c ^{2} t ^{2} g ^{2} \times 7 8 ^{6} c ^{5} t ^{5} g ^{5}}

Calculate

\frac{7 7 \times 7 8 ^{6} c ^{5} t ^{5} g ^{5}}{8 c t g}

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

\frac{7 7 \times 8 ^{6} c ^{5} t ^{5} g ^{5}}{8 c t g}

x = \frac{7 7 \times 8 ^{6} c ^{5} t ^{5} g ^{5}}{8 c t g}

Solution

More Steps

Evaluate

\frac{7 7 \times 8 ^{6} c ^{5} t ^{5} g ^{5}}{8 c t g}

Rewrite the expression

More Steps

Evaluate

7 7 \times 8^{6} c^{5} t^{5} g^{5}

Rewrite the expression

77 \times 7 8^{6} \times 7 c^{5} \times 7 t^{5} \times 7 g^{5}

Simplify the root

2^{2} 7 112 c^{5} t^{5} g^{5}

\frac{2 ^{2} 7 112 c ^{5} t ^{5} g ^{5}}{8 c t g}

Reduce the fraction

\frac{7 112 c ^{5} t ^{5} g ^{5}}{2 c t g}

x = \frac{7 112 c ^{5} t ^{5} g ^{5}}{2 c t g}

Show Solution