Solve 6x^(2) 7x-3

Question

Simplify the expression

42 x^{3} - 3

Evaluate

6 x^{2} \times 7 x - 3

Solution

More Steps

Evaluate

6 x^{2} \times 7 x

Multiply the terms

42 x^{2} \times x

Multiply the terms with the same base by adding their exponents

42 x^{2 + 1}

Add the numbers

42 x^{3}

42 x^{3} - 3

Show Solution

Factor the expression

3 (14 x^{3} - 1)

Evaluate

6 x^{2} \times 7 x - 3

Multiply

More Steps

Evaluate

6 x^{2} \times 7 x

Multiply the terms

42 x^{2} \times x

Multiply the terms with the same base by adding their exponents

42 x^{2 + 1}

Add the numbers

42 x^{3}

42 x^{3} - 3

Solution

3 (14 x^{3} - 1)

Show Solution

Find the roots

x = \frac{3 196}{14}

Alternative Form

x \approx 0.414913

Evaluate

6 x^{2} \times 7 x - 3

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

6 x^{2} \times 7 x - 3 = 0

Multiply

More Steps

Multiply the terms

6 x^{2} \times 7 x

Multiply the terms

42 x^{2} \times x

Multiply the terms with the same base by adding their exponents

42 x^{2 + 1}

Add the numbers

42 x^{3}

42 x^{3} - 3 = 0

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

42 x^{3} = 0 + 3

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

42 x^{3} = 3

Divide both sides

\frac{42 x ^{3}}{42} = \frac{3}{42}

Divide the numbers

x^{3} = \frac{3}{42}

Cancel out the common factor 3

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