Solve 2n^2 2n - 5

Question

Simplify the expression

4 n^{3} - 5

Evaluate

2 n^{2} \times 2 n - 5

Solution

More Steps

Evaluate

2 n^{2} \times 2 n

Multiply the terms

4 n^{2} \times n

Multiply the terms with the same base by adding their exponents

4 n^{2 + 1}

Add the numbers

4 n^{3}

4 n^{3} - 5

Show Solution

Find the roots

n = \frac{3 10}{2}

Alternative Form

n \approx 1.077217

Evaluate

2 n^{2} \times 2 n - 5

To find the roots of the expression,set the expression equal to 0

2 n^{2} \times 2 n - 5 = 0

Multiply

More Steps

Multiply the terms

2 n^{2} \times 2 n

Multiply the terms

4 n^{2} \times n

Multiply the terms with the same base by adding their exponents

4 n^{2 + 1}

Add the numbers

4 n^{3}

4 n^{3} - 5 = 0

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

4 n^{3} = 0 + 5

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

4 n^{3} = 5

Divide both sides

\frac{4 n ^{3}}{4} = \frac{5}{4}

Divide the numbers

n^{3} = \frac{5}{4}

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

3 n^{3} = 3 \frac{5}{4}

Calculate

n = 3 \frac{5}{4}

Solution

More Steps

Evaluate

3 \frac{5}{4}

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

\frac{3 5}{3 4}

Multiply by the Conjugate

\frac{3 5 \times 3 4 ^{2}}{3 4 \times 3 4 ^{2}}

Simplify

\frac{3 5 \times 2 3 2}{3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 232

Multiply the terms

310 \times 2

Use the commutative property to reorder the terms

2310

\frac{2 3 10}{3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

34 \times 3 4^{2}

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

3 4 \times 4^{2}

Calculate the product

3 4^{3}

Transform the expression

3 2^{6}

Reduce the index of the radical and exponent with 3

2^{2}

\frac{2 3 10}{2 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{2}{2 ^{2}}

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

\frac{1}{2 ^{2 - 1}}

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{3 10}{2}

n = \frac{3 10}{2}

Alternative Form

n \approx 1.077217

Show Solution