Solve 6x^2 10x - 5

Question

Simplify the expression

60 x^{3} - 5

Evaluate

6 x^{2} \times 10 x - 5

Solution

More Steps

Evaluate

6 x^{2} \times 10 x

Multiply the terms

60 x^{2} \times x

Multiply the terms with the same base by adding their exponents

60 x^{2 + 1}

Add the numbers

60 x^{3}

60 x^{3} - 5

Show Solution

Factor the expression

5 (12 x^{3} - 1)

Evaluate

6 x^{2} \times 10 x - 5

Multiply

More Steps

Evaluate

6 x^{2} \times 10 x

Multiply the terms

60 x^{2} \times x

Multiply the terms with the same base by adding their exponents

60 x^{2 + 1}

Add the numbers

60 x^{3}

60 x^{3} - 5

Solution

5 (12 x^{3} - 1)

Show Solution

Find the roots

x = \frac{3 18}{6}

Alternative Form

x \approx 0.43679

Evaluate

6 x^{2} \times 10 x - 5

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

6 x^{2} \times 10 x - 5 = 0

Multiply

More Steps

Multiply the terms

6 x^{2} \times 10 x

Multiply the terms

60 x^{2} \times x

Multiply the terms with the same base by adding their exponents

60 x^{2 + 1}

Add the numbers

60 x^{3}

60 x^{3} - 5 = 0

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

60 x^{3} = 0 + 5

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

60 x^{3} = 5

Divide both sides

\frac{60 x ^{3}}{60} = \frac{5}{60}

Divide the numbers

x^{3} = \frac{5}{60}

Cancel out the common factor 5

x^{3} = \frac{1}{12}

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

3 x^{3} = 3 \frac{1}{12}

Calculate

x = 3 \frac{1}{12}

Solution

More Steps

Evaluate

3 \frac{1}{12}

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

\frac{3 1}{3 12}

Simplify the radical expression

\frac{1}{3 12}

Multiply by the Conjugate

\frac{3 1 2 ^{2}}{3 12 \times 3 1 2 ^{2}}

Simplify

\frac{2 3 18}{3 12 \times 3 1 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

312 \times 3 1 2^{2}

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

3 12 \times 1 2^{2}

Calculate the product

3 1 2^{3}

Reduce the index of the radical and exponent with 3

12

\frac{2 3 18}{12}

Cancel out the common factor 2

\frac{3 18}{6}

x = \frac{3 18}{6}

Alternative Form

x \approx 0.43679

Show Solution