Solve 12x 10=5x 136x^6

Question

Solve the equation

x_{1} = - \frac{6 3 \times 1 7 ^{5}}{17}, x_{2} = 0, x_{3} = \frac{6 3 \times 1 7 ^{5}}{17}

Alternative Form

x_{1} \approx - 0.748937, x_{2} = 0, x_{3} \approx 0.748937

Evaluate

12 x \times 10 = 5 x \times 136 x^{6}

Multiply the terms

120 x = 5 x \times 136 x^{6}

Multiply

More Steps

Evaluate

5 x \times 136 x^{6}

Multiply the terms

680 x \times x^{6}

Multiply the terms with the same base by adding their exponents

680 x^{1 + 6}

Add the numbers

680 x^{7}

120 x = 680 x^{7}

Add or subtract both sides

120 x - 680 x^{7} = 0

Factor the expression

40 x (3 - 17 x^{6}) = 0

Divide both sides

x (3 - 17 x^{6}) = 0

Separate the equation into 2 possible cases

x = 0 3 - 17 x^{6} = 0

Solve the equation

More Steps

Evaluate

3 - 17 x^{6} = 0

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

- 17 x^{6} = 0 - 3

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

- 17 x^{6} = - 3

Change the signs on both sides of the equation

17 x^{6} = 3

Divide both sides

\frac{17 x ^{6}}{17} = \frac{3}{17}

Divide the numbers

x^{6} = \frac{3}{17}

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

x = \pm 6 \frac{3}{17}

Simplify the expression

More Steps

Evaluate

6 \frac{3}{17}

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

\frac{6 3}{6 17}

Multiply by the Conjugate

\frac{6 3 \times 6 1 7 ^{5}}{6 17 \times 6 1 7 ^{5}}

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

\frac{6 3 \times 1 7 ^{5}}{6 17 \times 6 1 7 ^{5}}

Multiply the numbers

\frac{6 3 \times 1 7 ^{5}}{17}

x = \pm \frac{6 3 \times 1 7 ^{5}}{17}

Separate the equation into 2 possible cases

x = \frac{6 3 \times 1 7 ^{5}}{17} x = - \frac{6 3 \times 1 7 ^{5}}{17}

x = 0 x = \frac{6 3 \times 1 7 ^{5}}{17} x = - \frac{6 3 \times 1 7 ^{5}}{17}

Solution

x_{1} = - \frac{6 3 \times 1 7 ^{5}}{17}, x_{2} = 0, x_{3} = \frac{6 3 \times 1 7 ^{5}}{17}

Alternative Form

x_{1} \approx - 0.748937, x_{2} = 0, x_{3} \approx 0.748937

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