Solve 3x^5x=400 - ScanMath

Question

Solve the equation

x_{1} = - \frac{6 97200}{3}, x_{2} = \frac{6 97200}{3}

Alternative Form

x_{1} \approx - 2.26025, x_{2} \approx 2.26025

Evaluate

3 x^{5} \times x = 400

Multiply

More Steps

Evaluate

3 x^{5} \times x

Multiply the terms with the same base by adding their exponents

3 x^{5 + 1}

Add the numbers

3 x^{6}

3 x^{6} = 400

Divide both sides

\frac{3 x ^{6}}{3} = \frac{400}{3}

Divide the numbers

x^{6} = \frac{400}{3}

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

x = \pm 6 \frac{400}{3}

Simplify the expression

More Steps

Evaluate

6 \frac{400}{3}

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

\frac{6 400}{6 3}

Simplify the radical expression

\frac{3 20}{6 3}

Multiply by the Conjugate

\frac{3 20 \times 6 3 ^{5}}{6 3 \times 6 3 ^{5}}

Simplify

\frac{3 20 \times 6 243}{6 3 \times 6 3 ^{5}}

Multiply the numbers

More Steps

Evaluate

320 \times 6243

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

6 2 0^{2} \times 6243

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

6 2 0^{2} \times 243

Calculate the product

697200

\frac{6 97200}{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 97200}{3}

x = \pm \frac{6 97200}{3}

Separate the equation into 2 possible cases

x = \frac{6 97200}{3} x = - \frac{6 97200}{3}

Solution

x_{1} = - \frac{6 97200}{3}, x_{2} = \frac{6 97200}{3}

Alternative Form

x_{1} \approx - 2.26025, x_{2} \approx 2.26025

Show Solution