Solve 6x^(2) 35x-56

Question

Simplify the expression

210 x^{3} - 56

Evaluate

6 x^{2} \times 35 x - 56

Solution

More Steps

Evaluate

6 x^{2} \times 35 x

Multiply the terms

210 x^{2} \times x

Multiply the terms with the same base by adding their exponents

210 x^{2 + 1}

Add the numbers

210 x^{3}

210 x^{3} - 56

Show Solution

Factor the expression

14 (15 x^{3} - 4)

Evaluate

6 x^{2} \times 35 x - 56

Multiply

More Steps

Evaluate

6 x^{2} \times 35 x

Multiply the terms

210 x^{2} \times x

Multiply the terms with the same base by adding their exponents

210 x^{2 + 1}

Add the numbers

210 x^{3}

210 x^{3} - 56

Solution

14 (15 x^{3} - 4)

Show Solution

Find the roots

x = \frac{3 900}{15}

Alternative Form

x \approx 0.64366

Evaluate

6 x^{2} \times 35 x - 56

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

6 x^{2} \times 35 x - 56 = 0

Multiply

More Steps

Multiply the terms

6 x^{2} \times 35 x

Multiply the terms

210 x^{2} \times x

Multiply the terms with the same base by adding their exponents

210 x^{2 + 1}

Add the numbers

210 x^{3}

210 x^{3} - 56 = 0

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

210 x^{3} = 0 + 56

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

210 x^{3} = 56

Divide both sides

\frac{210 x ^{3}}{210} = \frac{56}{210}

Divide the numbers

x^{3} = \frac{56}{210}

Cancel out the common factor 14

x^{3} = \frac{4}{15}

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

3 x^{3} = 3 \frac{4}{15}

Calculate

x = 3 \frac{4}{15}

Solution

More Steps

Evaluate

3 \frac{4}{15}

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

\frac{3 4}{3 15}

Multiply by the Conjugate

\frac{3 4 \times 3 1 5 ^{2}}{3 15 \times 3 1 5 ^{2}}

Simplify

\frac{3 4 \times 3 225}{3 15 \times 3 1 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

34 \times 3225

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

3 4 \times 225

Calculate the product

3900

\frac{3 900}{3 15 \times 3 1 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

315 \times 3 1 5^{2}

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

3 15 \times 1 5^{2}

Calculate the product

3 1 5^{3}

Reduce the index of the radical and exponent with 3

15

\frac{3 900}{15}

x = \frac{3 900}{15}

Alternative Form

x \approx 0.64366

Show Solution