Solve 12x ^ 2 7x - 10

Question

Simplify the expression

84 x^{3} - 10

Evaluate

12 x^{2} \times 7 x - 10

Solution

More Steps

Evaluate

12 x^{2} \times 7 x

Multiply the terms

84 x^{2} \times x

Multiply the terms with the same base by adding their exponents

84 x^{2 + 1}

Add the numbers

84 x^{3}

84 x^{3} - 10

Show Solution

Factor the expression

2 (42 x^{3} - 5)

Evaluate

12 x^{2} \times 7 x - 10

Multiply

More Steps

Evaluate

12 x^{2} \times 7 x

Multiply the terms

84 x^{2} \times x

Multiply the terms with the same base by adding their exponents

84 x^{2 + 1}

Add the numbers

84 x^{3}

84 x^{3} - 10

Solution

2 (42 x^{3} - 5)

Show Solution

Find the roots

x = \frac{3 8820}{42}

Alternative Form

x \approx 0.491934

Evaluate

12 x^{2} \times 7 x - 10

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

12 x^{2} \times 7 x - 10 = 0

Multiply

More Steps

Multiply the terms

12 x^{2} \times 7 x

Multiply the terms

84 x^{2} \times x

Multiply the terms with the same base by adding their exponents

84 x^{2 + 1}

Add the numbers

84 x^{3}

84 x^{3} - 10 = 0

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

84 x^{3} = 0 + 10

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

84 x^{3} = 10

Divide both sides

\frac{84 x ^{3}}{84} = \frac{10}{84}

Divide the numbers

x^{3} = \frac{10}{84}

Cancel out the common factor 2

x^{3} = \frac{5}{42}

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

3 x^{3} = 3 \frac{5}{42}

Calculate

x = 3 \frac{5}{42}

Solution

More Steps

Evaluate

3 \frac{5}{42}

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

\frac{3 5}{3 42}

Multiply by the Conjugate

\frac{3 5 \times 3 4 2 ^{2}}{3 42 \times 3 4 2 ^{2}}

Simplify

\frac{3 5 \times 3 1764}{3 42 \times 3 4 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 31764

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

3 5 \times 1764

Calculate the product

38820

\frac{3 8820}{3 42 \times 3 4 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

342 \times 3 4 2^{2}

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

3 42 \times 4 2^{2}

Calculate the product

3 4 2^{3}

Reduce the index of the radical and exponent with 3

42

\frac{3 8820}{42}

x = \frac{3 8820}{42}

Alternative Form

x \approx 0.491934

Show Solution