Solve 3x^503x^474x^38=180

Question

Solve the equation

x_{1} = - \frac{12 5 \times 14 8 ^{11}}{148}, x_{2} = \frac{12 5 \times 14 8 ^{11}}{148}

Alternative Form

x_{1} \approx - 0.754036, x_{2} \approx 0.754036

Evaluate

3 x^{5} \times 3 x^{4} \times 74 x^{3} \times 8 = 180

Multiply

More Steps

Evaluate

3 x^{5} \times 3 x^{4} \times 74 x^{3} \times 8

Multiply the terms

More Steps

Evaluate

3 \times 3 \times 74 \times 8

Multiply the terms

9 \times 74 \times 8

Multiply the terms

666 \times 8

Multiply the numbers

5328

5328 x^{5} \times x^{4} \times x^{3}

Multiply the terms with the same base by adding their exponents

5328 x^{5 + 4 + 3}

Add the numbers

5328 x^{12}

5328 x^{12} = 180

Divide both sides

\frac{5328 x ^{12}}{5328} = \frac{180}{5328}

Divide the numbers

x^{12} = \frac{180}{5328}

Cancel out the common factor 36

x^{12} = \frac{5}{148}

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

x = \pm 12 \frac{5}{148}

Simplify the expression

More Steps

Evaluate

12 \frac{5}{148}

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

\frac{12 5}{12 148}

Multiply by the Conjugate

\frac{12 5 \times 12 14 8 ^{11}}{12 148 \times 12 14 8 ^{11}}

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

\frac{12 5 \times 14 8 ^{11}}{12 148 \times 12 14 8 ^{11}}

Multiply the numbers

More Steps

Evaluate

12148 \times 12 14 8^{11}

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

12 148 \times 14 8^{11}

Calculate the product

12 14 8^{12}

Reduce the index of the radical and exponent with 12

148

\frac{12 5 \times 14 8 ^{11}}{148}

x = \pm \frac{12 5 \times 14 8 ^{11}}{148}

Separate the equation into 2 possible cases

x = \frac{12 5 \times 14 8 ^{11}}{148} x = - \frac{12 5 \times 14 8 ^{11}}{148}

Solution

x_{1} = - \frac{12 5 \times 14 8 ^{11}}{148}, x_{2} = \frac{12 5 \times 14 8 ^{11}}{148}

Alternative Form

x_{1} \approx - 0.754036, x_{2} \approx 0.754036

Show Solution