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

Question

Solve the equation

x_{1} = - \frac{6 132192}{6}, x_{2} = \frac{6 132192}{6}

Alternative Form

x_{1} \approx - 1.189551, x_{2} \approx 1.189551

Evaluate

3 \times 3 x^{6} \times 2 - 46 = 5

Multiply the terms

More Steps

Evaluate

3 \times 3 \times 2

Multiply the terms

9 \times 2

Multiply the numbers

18

18 x^{6} - 46 = 5

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

18 x^{6} = 5 + 46

Add the numbers

18 x^{6} = 51

Divide both sides

\frac{18 x ^{6}}{18} = \frac{51}{18}

Divide the numbers

x^{6} = \frac{51}{18}

Cancel out the common factor 3

x^{6} = \frac{17}{6}

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

x = \pm 6 \frac{17}{6}

Simplify the expression

More Steps

Evaluate

6 \frac{17}{6}

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

\frac{6 17}{6 6}

Multiply by the Conjugate

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

Simplify

\frac{6 17 \times 6 7776}{6 6 \times 6 6 ^{5}}

Multiply the numbers

More Steps

Evaluate

617 \times 67776

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

6 17 \times 7776

Calculate the product

6132192

\frac{6 132192}{6 6 \times 6 6 ^{5}}

Multiply the numbers

More Steps

Evaluate

66 \times 6 6^{5}

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

6 6 \times 6^{5}

Calculate the product

6 6^{6}

Reduce the index of the radical and exponent with 6

6

\frac{6 132192}{6}

x = \pm \frac{6 132192}{6}

Separate the equation into 2 possible cases

x = \frac{6 132192}{6} x = - \frac{6 132192}{6}

Solution

x_{1} = - \frac{6 132192}{6}, x_{2} = \frac{6 132192}{6}

Alternative Form

x_{1} \approx - 1.189551, x_{2} \approx 1.189551

Show Solution