Solve 3x^(2) 6x-45

Question

Simplify the expression

18 x^{3} - 45

Evaluate

3 x^{2} \times 6 x - 45

Solution

More Steps

Evaluate

3 x^{2} \times 6 x

Multiply the terms

18 x^{2} \times x

Multiply the terms with the same base by adding their exponents

18 x^{2 + 1}

Add the numbers

18 x^{3}

18 x^{3} - 45

Show Solution

Factor the expression

9 (2 x^{3} - 5)

Evaluate

3 x^{2} \times 6 x - 45

Multiply

More Steps

Evaluate

3 x^{2} \times 6 x

Multiply the terms

18 x^{2} \times x

Multiply the terms with the same base by adding their exponents

18 x^{2 + 1}

Add the numbers

18 x^{3}

18 x^{3} - 45

Solution

9 (2 x^{3} - 5)

Show Solution

Find the roots

x = \frac{3 20}{2}

Alternative Form

x \approx 1.357209

Evaluate

3 x^{2} \times 6 x - 45

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

3 x^{2} \times 6 x - 45 = 0

Multiply

More Steps

Multiply the terms

3 x^{2} \times 6 x

Multiply the terms

18 x^{2} \times x

Multiply the terms with the same base by adding their exponents

18 x^{2 + 1}

Add the numbers

18 x^{3}

18 x^{3} - 45 = 0

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

18 x^{3} = 0 + 45

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

18 x^{3} = 45

Divide both sides

\frac{18 x ^{3}}{18} = \frac{45}{18}

Divide the numbers

x^{3} = \frac{45}{18}

Cancel out the common factor 9

x^{3} = \frac{5}{2}

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

3 x^{3} = 3 \frac{5}{2}

Calculate

x = 3 \frac{5}{2}

Solution

More Steps

Evaluate

3 \frac{5}{2}

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

\frac{3 5}{3 2}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

More Steps

Evaluate

35 \times 34

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

3 5 \times 4

Calculate the product

320

\frac{3 20}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 20}{2}

x = \frac{3 20}{2}

Alternative Form

x \approx 1.357209

Show Solution