Solve 2n^2 5n-525

Question

Simplify the expression

10 n^{3} - 525

Evaluate

2 n^{2} \times 5 n - 525

Solution

More Steps

Evaluate

2 n^{2} \times 5 n

Multiply the terms

10 n^{2} \times n

Multiply the terms with the same base by adding their exponents

10 n^{2 + 1}

Add the numbers

10 n^{3}

10 n^{3} - 525

Show Solution

Factor the expression

5 (2 n^{3} - 105)

Evaluate

2 n^{2} \times 5 n - 525

Multiply

More Steps

Evaluate

2 n^{2} \times 5 n

Multiply the terms

10 n^{2} \times n

Multiply the terms with the same base by adding their exponents

10 n^{2 + 1}

Add the numbers

10 n^{3}

10 n^{3} - 525

Solution

5 (2 n^{3} - 105)

Show Solution

Find the roots

n = \frac{3 420}{2}

Alternative Form

n \approx 3.744436

Evaluate

2 n^{2} \times 5 n - 525

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

2 n^{2} \times 5 n - 525 = 0

Multiply

More Steps

Multiply the terms

2 n^{2} \times 5 n

Multiply the terms

10 n^{2} \times n

Multiply the terms with the same base by adding their exponents

10 n^{2 + 1}

Add the numbers

10 n^{3}

10 n^{3} - 525 = 0

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

10 n^{3} = 0 + 525

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

10 n^{3} = 525

Divide both sides

\frac{10 n ^{3}}{10} = \frac{525}{10}

Divide the numbers

n^{3} = \frac{525}{10}

Cancel out the common factor 5

n^{3} = \frac{105}{2}

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

3 n^{3} = 3 \frac{105}{2}

Calculate

n = 3 \frac{105}{2}

Solution

More Steps

Evaluate

3 \frac{105}{2}

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

\frac{3 105}{3 2}

Multiply by the Conjugate

\frac{3 105 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{3 105 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

3105 \times 34

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

3 105 \times 4

Calculate the product

3420

\frac{3 420}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 420}{2}

n = \frac{3 420}{2}

Alternative Form

n \approx 3.744436

Show Solution