Solve 3x^2 4x-28 - ScanMath

Question

Simplify the expression

12 x^{3} - 28

Evaluate

3 x^{2} \times 4 x - 28

Solution

More Steps

Evaluate

3 x^{2} \times 4 x

Multiply the terms

12 x^{2} \times x

Multiply the terms with the same base by adding their exponents

12 x^{2 + 1}

Add the numbers

12 x^{3}

12 x^{3} - 28

Show Solution

Factor the expression

4 (3 x^{3} - 7)

Evaluate

3 x^{2} \times 4 x - 28

Multiply

More Steps

Evaluate

3 x^{2} \times 4 x

Multiply the terms

12 x^{2} \times x

Multiply the terms with the same base by adding their exponents

12 x^{2 + 1}

Add the numbers

12 x^{3}

12 x^{3} - 28

Solution

4 (3 x^{3} - 7)

Show Solution

Find the roots

x = \frac{3 63}{3}

Alternative Form

x \approx 1.326352

Evaluate

3 x^{2} \times 4 x - 28

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

3 x^{2} \times 4 x - 28 = 0

Multiply

More Steps

Multiply the terms

3 x^{2} \times 4 x

Multiply the terms

12 x^{2} \times x

Multiply the terms with the same base by adding their exponents

12 x^{2 + 1}

Add the numbers

12 x^{3}

12 x^{3} - 28 = 0

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

12 x^{3} = 0 + 28

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

12 x^{3} = 28

Divide both sides

\frac{12 x ^{3}}{12} = \frac{28}{12}

Divide the numbers

x^{3} = \frac{28}{12}

Cancel out the common factor 4

x^{3} = \frac{7}{3}

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

3 x^{3} = 3 \frac{7}{3}

Calculate

x = 3 \frac{7}{3}

Solution

More Steps

Evaluate

3 \frac{7}{3}

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

\frac{3 7}{3 3}

Multiply by the Conjugate

\frac{3 7 \times 3 3 ^{2}}{3 3 \times 3 3 ^{2}}

Simplify

\frac{3 7 \times 3 9}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 39

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

3 7 \times 9

Calculate the product

363

\frac{3 63}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 3 3^{2}

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

3 3 \times 3^{2}

Calculate the product

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{3 63}{3}

x = \frac{3 63}{3}

Alternative Form

x \approx 1.326352

Show Solution