Solve 4x^2 12x-172

Question

Simplify the expression

48 x^{3} - 172

Evaluate

4 x^{2} \times 12 x - 172

Solution

More Steps

Evaluate

4 x^{2} \times 12 x

Multiply the terms

48 x^{2} \times x

Multiply the terms with the same base by adding their exponents

48 x^{2 + 1}

Add the numbers

48 x^{3}

48 x^{3} - 172

Show Solution

Factor the expression

4 (12 x^{3} - 43)

Evaluate

4 x^{2} \times 12 x - 172

Multiply

More Steps

Evaluate

4 x^{2} \times 12 x

Multiply the terms

48 x^{2} \times x

Multiply the terms with the same base by adding their exponents

48 x^{2 + 1}

Add the numbers

48 x^{3}

48 x^{3} - 172

Solution

4 (12 x^{3} - 43)

Show Solution

Find the roots

x = \frac{3 774}{6}

Alternative Form

x \approx 1.53025

Evaluate

4 x^{2} \times 12 x - 172

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

4 x^{2} \times 12 x - 172 = 0

Multiply

More Steps

Multiply the terms

4 x^{2} \times 12 x

Multiply the terms

48 x^{2} \times x

Multiply the terms with the same base by adding their exponents

48 x^{2 + 1}

Add the numbers

48 x^{3}

48 x^{3} - 172 = 0

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

48 x^{3} = 0 + 172

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

48 x^{3} = 172

Divide both sides

\frac{48 x ^{3}}{48} = \frac{172}{48}

Divide the numbers

x^{3} = \frac{172}{48}

Cancel out the common factor 4

x^{3} = \frac{43}{12}

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

3 x^{3} = 3 \frac{43}{12}

Calculate

x = 3 \frac{43}{12}

Solution

More Steps

Evaluate

3 \frac{43}{12}

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

\frac{3 43}{3 12}

Multiply by the Conjugate

\frac{3 43 \times 3 1 2 ^{2}}{3 12 \times 3 1 2 ^{2}}

Simplify

\frac{3 43 \times 2 3 18}{3 12 \times 3 1 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

343 \times 2318

Multiply the terms

3774 \times 2

Use the commutative property to reorder the terms

23774

\frac{2 3 774}{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 3 774}{12}

Cancel out the common factor 2

\frac{3 774}{6}

x = \frac{3 774}{6}

Alternative Form

x \approx 1.53025

Show Solution