Solve 82n^2674n=599(27n 93)

Question

Solve the equation

n_{1} = - \frac{9 256567873}{27634}, n_{2} = 0, n_{3} = \frac{9 256567873}{27634}

Alternative Form

n_{1} \approx - 5.216748, n_{2} = 0, n_{3} \approx 5.216748

Evaluate

82 n^{2} \times 674 n = 599 (27 n \times 93)

Remove the parentheses

82 n^{2} \times 674 n = 599 \times 27 n \times 93

Multiply

More Steps

Evaluate

82 n^{2} \times 674 n

Multiply the terms

55268 n^{2} \times n

Multiply the terms with the same base by adding their exponents

55268 n^{2 + 1}

Add the numbers

55268 n^{3}

55268 n^{3} = 599 \times 27 n \times 93

Multiply the terms

More Steps

Evaluate

599 \times 27 \times 93

Multiply the terms

16173 \times 93

Multiply the numbers

1504089

55268 n^{3} = 1504089 n

Add or subtract both sides

55268 n^{3} - 1504089 n = 0

Factor the expression

n (55268 n^{2} - 1504089) = 0

Separate the equation into 2 possible cases

n = 0 55268 n^{2} - 1504089 = 0

Solve the equation

More Steps

Evaluate

55268 n^{2} - 1504089 = 0

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

55268 n^{2} = 0 + 1504089

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

55268 n^{2} = 1504089

Divide both sides

\frac{55268 n ^{2}}{55268} = \frac{1504089}{55268}

Divide the numbers

n^{2} = \frac{1504089}{55268}

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

n = \pm \frac{1504089}{55268}

Simplify the expression

More Steps

Evaluate

\frac{1504089}{55268}

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

\frac{1504089}{55268}

Simplify the radical expression

\frac{9 18569}{55268}

Simplify the radical expression

\frac{9 18569}{2 13817}

Multiply by the Conjugate

\frac{9 18569 \times 13817}{2 13817 \times 13817}

Multiply the numbers

\frac{9 256567873}{2 13817 \times 13817}

Multiply the numbers

\frac{9 256567873}{27634}

n = \pm \frac{9 256567873}{27634}

Separate the equation into 2 possible cases

n = \frac{9 256567873}{27634} n = - \frac{9 256567873}{27634}

n = 0 n = \frac{9 256567873}{27634} n = - \frac{9 256567873}{27634}

Solution

n_{1} = - \frac{9 256567873}{27634}, n_{2} = 0, n_{3} = \frac{9 256567873}{27634}

Alternative Form

n_{1} \approx - 5.216748, n_{2} = 0, n_{3} \approx 5.216748

Show Solution