Solve 30x^27x-15 - ScanMath

Question

Simplify the expression

210 x^{3} - 15

Evaluate

30 x^{2} \times 7 x - 15

Solution

More Steps

Evaluate

30 x^{2} \times 7 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} - 15

Show Solution

Factor the expression

15 (14 x^{3} - 1)

Evaluate

30 x^{2} \times 7 x - 15

Multiply

More Steps

Evaluate

30 x^{2} \times 7 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} - 15

Solution

15 (14 x^{3} - 1)

Show Solution

Find the roots

x = \frac{3 196}{14}

Alternative Form

x \approx 0.414913

Evaluate

30 x^{2} \times 7 x - 15

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

30 x^{2} \times 7 x - 15 = 0

Multiply

More Steps

Multiply the terms

30 x^{2} \times 7 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} - 15 = 0

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

210 x^{3} = 0 + 15

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

210 x^{3} = 15

Divide both sides

\frac{210 x ^{3}}{210} = \frac{15}{210}

Divide the numbers

x^{3} = \frac{15}{210}

Cancel out the common factor 15

x^{3} = \frac{1}{14}

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

3 x^{3} = 3 \frac{1}{14}

Calculate

x = 3 \frac{1}{14}

Solution

More Steps

Evaluate

3 \frac{1}{14}

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

\frac{3 1}{3 14}

Simplify the radical expression

\frac{1}{3 14}

Multiply by the Conjugate

\frac{3 1 4 ^{2}}{3 14 \times 3 1 4 ^{2}}

Simplify

\frac{3 196}{3 14 \times 3 1 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

314 \times 3 1 4^{2}

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

3 14 \times 1 4^{2}

Calculate the product

3 1 4^{3}

Reduce the index of the radical and exponent with 3

14

\frac{3 196}{14}

x = \frac{3 196}{14}

Alternative Form

x \approx 0.414913

Show Solution