Solve 2n^2 9n-41=0

Question

Solve the equation

n = \frac{3 492}{6}

Alternative Form

n \approx 1.315741

Evaluate

2 n^{2} \times 9 n - 41 = 0

Multiply

More Steps

Evaluate

2 n^{2} \times 9 n

Multiply the terms

18 n^{2} \times n

Multiply the terms with the same base by adding their exponents

18 n^{2 + 1}

Add the numbers

18 n^{3}

18 n^{3} - 41 = 0

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

18 n^{3} = 0 + 41

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

18 n^{3} = 41

Divide both sides

\frac{18 n ^{3}}{18} = \frac{41}{18}

Divide the numbers

n^{3} = \frac{41}{18}

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

3 n^{3} = 3 \frac{41}{18}

Calculate

n = 3 \frac{41}{18}

Solution

More Steps

Evaluate

3 \frac{41}{18}

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

\frac{3 41}{3 18}

Multiply by the Conjugate

\frac{3 41 \times 3 1 8 ^{2}}{3 18 \times 3 1 8 ^{2}}

Simplify

\frac{3 41 \times 3 3 12}{3 18 \times 3 1 8 ^{2}}

Multiply the numbers

More Steps

Evaluate

341 \times 3312

Multiply the terms

3492 \times 3

Use the commutative property to reorder the terms

33492

\frac{3 3 492}{3 18 \times 3 1 8 ^{2}}

Multiply the numbers

More Steps

Evaluate

318 \times 3 1 8^{2}

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

3 18 \times 1 8^{2}

Calculate the product

3 1 8^{3}

Reduce the index of the radical and exponent with 3

18

\frac{3 3 492}{18}

Cancel out the common factor 3

\frac{3 492}{6}

n = \frac{3 492}{6}

Alternative Form

n \approx 1.315741

Show Solution