Solve 3(3x^6) ^2 -46=5

Question

Solve the equation

x_{1} = - \frac{12 1003833}{3}, x_{2} = \frac{12 1003833}{3}

Alternative Form

x_{1} \approx - 1.054429, x_{2} \approx 1.054429

Evaluate

3 (3 x^{6})^{2} - 46 = 5

Multiply the terms

More Steps

Evaluate

3 (3 x^{6})^{2}

Rewrite the expression

3 \times 9 x^{12}

Multiply the numbers

27 x^{12}

27 x^{12} - 46 = 5

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

27 x^{12} = 5 + 46

Add the numbers

27 x^{12} = 51

Divide both sides

\frac{27 x ^{12}}{27} = \frac{51}{27}

Divide the numbers

x^{12} = \frac{51}{27}

Cancel out the common factor 3

x^{12} = \frac{17}{9}

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

x = \pm 12 \frac{17}{9}

Simplify the expression

More Steps

Evaluate

12 \frac{17}{9}

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

\frac{12 17}{12 9}

Simplify the radical expression

More Steps

Evaluate

129

Write the number in exponential form with the base of 3

12 3^{2}

Reduce the index of the radical and exponent with 2

63

\frac{12 17}{6 3}

Multiply by the Conjugate

\frac{12 17 \times 6 3 ^{5}}{6 3 \times 6 3 ^{5}}

Simplify

\frac{12 17 \times 6 243}{6 3 \times 6 3 ^{5}}

Multiply the numbers

More Steps

Evaluate

1217 \times 6243

Use n a = mn a^{m} to expand the expression

1217 \times 12 24 3^{2}

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

12 17 \times 24 3^{2}

Calculate the product

121003833

\frac{12 1003833}{6 3 \times 6 3 ^{5}}

Multiply the numbers

More Steps

Evaluate

63 \times 6 3^{5}

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

6 3 \times 3^{5}

Calculate the product

6 3^{6}

Reduce the index of the radical and exponent with 6

3

\frac{12 1003833}{3}

x = \pm \frac{12 1003833}{3}

Separate the equation into 2 possible cases

x = \frac{12 1003833}{3} x = - \frac{12 1003833}{3}

Solution

x_{1} = - \frac{12 1003833}{3}, x_{2} = \frac{12 1003833}{3}

Alternative Form

x_{1} \approx - 1.054429, x_{2} \approx 1.054429

Show Solution