Solve 2x^2350x-6000

Question

Simplify the expression

700 x^{3} - 6000

Evaluate

2 x^{2} \times 350 x - 6000

Solution

More Steps

Evaluate

2 x^{2} \times 350 x

Multiply the terms

700 x^{2} \times x

Multiply the terms with the same base by adding their exponents

700 x^{2 + 1}

Add the numbers

700 x^{3}

700 x^{3} - 6000

Show Solution

Factor the expression

100 (7 x^{3} - 60)

Evaluate

2 x^{2} \times 350 x - 6000

Multiply

More Steps

Evaluate

2 x^{2} \times 350 x

Multiply the terms

700 x^{2} \times x

Multiply the terms with the same base by adding their exponents

700 x^{2 + 1}

Add the numbers

700 x^{3}

700 x^{3} - 6000

Solution

100 (7 x^{3} - 60)

Show Solution

Find the roots

x = \frac{3 2940}{7}

Alternative Form

x \approx 2.046528

Evaluate

2 x^{2} \times 350 x - 6000

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

2 x^{2} \times 350 x - 6000 = 0

Multiply

More Steps

Multiply the terms

2 x^{2} \times 350 x

Multiply the terms

700 x^{2} \times x

Multiply the terms with the same base by adding their exponents

700 x^{2 + 1}

Add the numbers

700 x^{3}

700 x^{3} - 6000 = 0

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

700 x^{3} = 0 + 6000

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

700 x^{3} = 6000

Divide both sides

\frac{700 x ^{3}}{700} = \frac{6000}{700}

Divide the numbers

x^{3} = \frac{6000}{700}

Cancel out the common factor 100

x^{3} = \frac{60}{7}

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

3 x^{3} = 3 \frac{60}{7}

Calculate

x = 3 \frac{60}{7}

Solution

More Steps

Evaluate

3 \frac{60}{7}

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

\frac{3 60}{3 7}

Multiply by the Conjugate

\frac{3 60 \times 3 7 ^{2}}{3 7 \times 3 7 ^{2}}

Simplify

\frac{3 60 \times 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

360 \times 349

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

3 60 \times 49

Calculate the product

32940

\frac{3 2940}{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 2940}{7}

x = \frac{3 2940}{7}

Alternative Form

x \approx 2.046528

Show Solution