Solve 3x^52x=20 - ScanMath

Question

Solve the equation

x_{1} = - \frac{6 2430}{3}, x_{2} = \frac{6 2430}{3}

Alternative Form

x_{1} \approx - 1.222212, x_{2} \approx 1.222212

Evaluate

3 x^{5} \times 2 x = 20

Multiply

More Steps

Evaluate

3 x^{5} \times 2 x

Multiply the terms

6 x^{5} \times x

Multiply the terms with the same base by adding their exponents

6 x^{5 + 1}

Add the numbers

6 x^{6}

6 x^{6} = 20

Divide both sides

\frac{6 x ^{6}}{6} = \frac{20}{6}

Divide the numbers

x^{6} = \frac{20}{6}

Cancel out the common factor 2

x^{6} = \frac{10}{3}

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

x = \pm 6 \frac{10}{3}

Simplify the expression

More Steps

Evaluate

6 \frac{10}{3}

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

\frac{6 10}{6 3}

Multiply by the Conjugate

\frac{6 10 \times 6 3 ^{5}}{6 3 \times 6 3 ^{5}}

Simplify

\frac{6 10 \times 6 243}{6 3 \times 6 3 ^{5}}

Multiply the numbers

More Steps

Evaluate

610 \times 6243

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

6 10 \times 243

Calculate the product

62430

\frac{6 2430}{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{6 2430}{3}

x = \pm \frac{6 2430}{3}

Separate the equation into 2 possible cases

x = \frac{6 2430}{3} x = - \frac{6 2430}{3}

Solution

x_{1} = - \frac{6 2430}{3}, x_{2} = \frac{6 2430}{3}

Alternative Form

x_{1} \approx - 1.222212, x_{2} \approx 1.222212

Show Solution