Solve (2 (x 1) (x^2) (x^3))*x^2=(3(x^2)(x^3)(x^4))*x^

Question

Solve the equation

x_{1} = 0, x_{2} = \frac{3 18}{3}

Alternative Form

x_{1} = 0, x_{2} \approx 0.87358

Evaluate

(2 (x \times 1) x^{2} \times x^{3}) x^{2} = (3 x^{2} \times x^{3} \times x^{4}) x^{2}

Remove the parentheses

2 x \times 1 \times x^{2} \times x^{3} \times x^{2} = 3 x^{2} \times x^{3} \times x^{4} \times x^{2}

Multiply the terms

More Steps

Evaluate

2 x \times 1 \times x^{2} \times x^{3} \times x^{2}

Rewrite the expression

2 x \times x^{2} \times x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

2 x^{1 + 2 + 3 + 2}

Add the numbers

2 x^{8}

2 x^{8} = 3 x^{2} \times x^{3} \times x^{4} \times x^{2}

Multiply

More Steps

Evaluate

3 x^{2} \times x^{3} \times x^{4} \times x^{2}

Multiply the terms with the same base by adding their exponents

3 x^{2 + 3 + 4 + 2}

Add the numbers

3 x^{11}

2 x^{8} = 3 x^{11}

Add or subtract both sides

2 x^{8} - 3 x^{11} = 0

Factor the expression

x^{8} (2 - 3 x^{3}) = 0

Separate the equation into 2 possible cases

x^{8} = 0 2 - 3 x^{3} = 0

The only way a power can be 0 is when the base equals 0

x = 0 2 - 3 x^{3} = 0

Solve the equation

More Steps

Evaluate

2 - 3 x^{3} = 0

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

- 3 x^{3} = 0 - 2

Removing 0 doesn't change the value,so remove it from the expression

- 3 x^{3} = - 2

Change the signs on both sides of the equation

3 x^{3} = 2

Divide both sides

\frac{3 x ^{3}}{3} = \frac{2}{3}

Divide the numbers

x^{3} = \frac{2}{3}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{2}{3}

Calculate

x = 3 \frac{2}{3}

Simplify the root

More Steps

Evaluate

3 \frac{2}{3}

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

\frac{3 2}{3 3}

Multiply by the Conjugate

\frac{3 2 \times 3 3 ^{2}}{3 3 \times 3 3 ^{2}}

Simplify

\frac{3 2 \times 3 9}{3 3 \times 3 3 ^{2}}

Multiply the numbers

\frac{3 18}{3 3 \times 3 3 ^{2}}

Multiply the numbers

\frac{3 18}{3}

x = \frac{3 18}{3}

x = 0 x = \frac{3 18}{3}

Solution

x_{1} = 0, x_{2} = \frac{3 18}{3}

Alternative Form

x_{1} = 0, x_{2} \approx 0.87358

Show Solution