Solve 2000x^6100x^5 x-2 = 0

Question

Solve the equation

x_{1} = - \frac{12 1 0 ^{7}}{10}, x_{2} = \frac{12 1 0 ^{7}}{10}

Alternative Form

x_{1} \approx - 0.383119, x_{2} \approx 0.383119

Evaluate

2000 x^{6} \times 100 x^{5} \times x - 2 = 0

Multiply

More Steps

Evaluate

2000 x^{6} \times 100 x^{5} \times x

Multiply the terms

200000 x^{6} \times x^{5} \times x

Multiply the terms with the same base by adding their exponents

200000 x^{6 + 5 + 1}

Add the numbers

200000 x^{12}

200000 x^{12} - 2 = 0

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

200000 x^{12} = 0 + 2

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

200000 x^{12} = 2

Divide both sides

\frac{200000 x ^{12}}{200000} = \frac{2}{200000}

Divide the numbers

x^{12} = \frac{2}{200000}

Cancel out the common factor 2

x^{12} = \frac{1}{100000}

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

x = \pm 12 \frac{1}{100000}

Simplify the expression

More Steps

Evaluate

12 \frac{1}{100000}

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

\frac{12 1}{12 100000}

Simplify the radical expression

\frac{1}{12 100000}

Multiply by the Conjugate

\frac{12 10000 0 ^{11}}{12 100000 \times 12 10000 0 ^{11}}

Simplify

\frac{1 0 ^{4} 12 1 0 ^{7}}{12 100000 \times 12 10000 0 ^{11}}

Multiply the numbers

More Steps

Evaluate

12100000 \times 12 10000 0^{11}

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

12 100000 \times 10000 0^{11}

Calculate the product

12 10000 0^{12}

Transform the expression

12 1 0^{60}

Reduce the index of the radical and exponent with 12

1 0^{5}

\frac{1 0 ^{4} 12 1 0 ^{7}}{1 0 ^{5}}

Reduce the fraction

More Steps

Evaluate

\frac{1 0 ^{4}}{1 0 ^{5}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{1 0 ^{5 - 4}}

Subtract the terms

\frac{1}{1 0 ^{1}}

Simplify

\frac{1}{10}

\frac{12 1 0 ^{7}}{10}

x = \pm \frac{12 1 0 ^{7}}{10}

Separate the equation into 2 possible cases

x = \frac{12 1 0 ^{7}}{10} x = - \frac{12 1 0 ^{7}}{10}

Solution

x_{1} = - \frac{12 1 0 ^{7}}{10}, x_{2} = \frac{12 1 0 ^{7}}{10}

Alternative Form

x_{1} \approx - 0.383119, x_{2} \approx 0.383119

Show Solution