Solve 5x^2 19x-30

Question

Simplify the expression

95 x^{3} - 30

Evaluate

5 x^{2} \times 19 x - 30

Solution

More Steps

Evaluate

5 x^{2} \times 19 x

Multiply the terms

95 x^{2} \times x

Multiply the terms with the same base by adding their exponents

95 x^{2 + 1}

Add the numbers

95 x^{3}

95 x^{3} - 30

Show Solution

Factor the expression

5 (19 x^{3} - 6)

Evaluate

5 x^{2} \times 19 x - 30

Multiply

More Steps

Evaluate

5 x^{2} \times 19 x

Multiply the terms

95 x^{2} \times x

Multiply the terms with the same base by adding their exponents

95 x^{2 + 1}

Add the numbers

95 x^{3}

95 x^{3} - 30

Solution

5 (19 x^{3} - 6)

Show Solution

Find the roots

x = \frac{3 2166}{19}

Alternative Form

x \approx 0.680977

Evaluate

5 x^{2} \times 19 x - 30

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

5 x^{2} \times 19 x - 30 = 0

Multiply

More Steps

Multiply the terms

5 x^{2} \times 19 x

Multiply the terms

95 x^{2} \times x

Multiply the terms with the same base by adding their exponents

95 x^{2 + 1}

Add the numbers

95 x^{3}

95 x^{3} - 30 = 0

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

95 x^{3} = 0 + 30

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

95 x^{3} = 30

Divide both sides

\frac{95 x ^{3}}{95} = \frac{30}{95}

Divide the numbers

x^{3} = \frac{30}{95}

Cancel out the common factor 5

x^{3} = \frac{6}{19}

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

3 x^{3} = 3 \frac{6}{19}

Calculate

x = 3 \frac{6}{19}

Solution

More Steps

Evaluate

3 \frac{6}{19}

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

\frac{3 6}{3 19}

Multiply by the Conjugate

\frac{3 6 \times 3 1 9 ^{2}}{3 19 \times 3 1 9 ^{2}}

Simplify

\frac{3 6 \times 3 361}{3 19 \times 3 1 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

36 \times 3361

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

3 6 \times 361

Calculate the product

32166

\frac{3 2166}{3 19 \times 3 1 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

319 \times 3 1 9^{2}

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

3 19 \times 1 9^{2}

Calculate the product

3 1 9^{3}

Reduce the index of the radical and exponent with 3

19

\frac{3 2166}{19}

x = \frac{3 2166}{19}

Alternative Form

x \approx 0.680977

Show Solution