Solve 180 = 2x^346x -6

Question

Solve the equation

x_{1} = - \frac{4 93 \times 4 6 ^{3}}{46}, x_{2} = \frac{4 93 \times 4 6 ^{3}}{46}

Alternative Form

x_{1} \approx - 1.192426, x_{2} \approx 1.192426

Evaluate

180 = 2 x^{3} \times 46 x - 6

Multiply

More Steps

Evaluate

2 x^{3} \times 46 x

Multiply the terms

92 x^{3} \times x

Multiply the terms with the same base by adding their exponents

92 x^{3 + 1}

Add the numbers

92 x^{4}

180 = 92 x^{4} - 6

Swap the sides of the equation

92 x^{4} - 6 = 180

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

92 x^{4} = 180 + 6

Add the numbers

92 x^{4} = 186

Divide both sides

\frac{92 x ^{4}}{92} = \frac{186}{92}

Divide the numbers

x^{4} = \frac{186}{92}

Cancel out the common factor 2

x^{4} = \frac{93}{46}

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

x = \pm 4 \frac{93}{46}

Simplify the expression

More Steps

Evaluate

4 \frac{93}{46}

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

\frac{4 93}{4 46}

Multiply by the Conjugate

\frac{4 93 \times 4 4 6 ^{3}}{4 46 \times 4 4 6 ^{3}}

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

\frac{4 93 \times 4 6 ^{3}}{4 46 \times 4 4 6 ^{3}}

Multiply the numbers

More Steps

Evaluate

446 \times 4 4 6^{3}

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

4 46 \times 4 6^{3}

Calculate the product

4 4 6^{4}

Reduce the index of the radical and exponent with 4

46

\frac{4 93 \times 4 6 ^{3}}{46}

x = \pm \frac{4 93 \times 4 6 ^{3}}{46}

Separate the equation into 2 possible cases

x = \frac{4 93 \times 4 6 ^{3}}{46} x = - \frac{4 93 \times 4 6 ^{3}}{46}

Solution

x_{1} = - \frac{4 93 \times 4 6 ^{3}}{46}, x_{2} = \frac{4 93 \times 4 6 ^{3}}{46}

Alternative Form

x_{1} \approx - 1.192426, x_{2} \approx 1.192426

Show Solution