Solve 2n^2 14n-340=0

Question

Solve the equation

n = \frac{3 4165}{7}

Alternative Form

n \approx 2.298478

Evaluate

2 n^{2} \times 14 n - 340 = 0

Multiply

More Steps

Evaluate

2 n^{2} \times 14 n

Multiply the terms

28 n^{2} \times n

Multiply the terms with the same base by adding their exponents

28 n^{2 + 1}

Add the numbers

28 n^{3}

28 n^{3} - 340 = 0

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

28 n^{3} = 0 + 340

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

28 n^{3} = 340

Divide both sides

\frac{28 n ^{3}}{28} = \frac{340}{28}

Divide the numbers

n^{3} = \frac{340}{28}

Cancel out the common factor 4

n^{3} = \frac{85}{7}

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

3 n^{3} = 3 \frac{85}{7}

Calculate

n = 3 \frac{85}{7}

Solution

More Steps

Evaluate

3 \frac{85}{7}

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

\frac{3 85}{3 7}

Multiply by the Conjugate

\frac{3 85 \times 3 7 ^{2}}{3 7 \times 3 7 ^{2}}

Simplify

\frac{3 85 \times 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

385 \times 349

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

3 85 \times 49

Calculate the product

34165

\frac{3 4165}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 3 7^{2}

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

3 7 \times 7^{2}

Calculate the product

3 7^{3}

Reduce the index of the radical and exponent with 3

7

\frac{3 4165}{7}

n = \frac{3 4165}{7}

Alternative Form

n \approx 2.298478

Show Solution