Solve 3x^2 15x-18

Question

Simplify the expression

45 x^{3} - 18

Evaluate

3 x^{2} \times 15 x - 18

Solution

More Steps

Evaluate

3 x^{2} \times 15 x

Multiply the terms

45 x^{2} \times x

Multiply the terms with the same base by adding their exponents

45 x^{2 + 1}

Add the numbers

45 x^{3}

45 x^{3} - 18

Show Solution

Factor the expression

9 (5 x^{3} - 2)

Evaluate

3 x^{2} \times 15 x - 18

Multiply

More Steps

Evaluate

3 x^{2} \times 15 x

Multiply the terms

45 x^{2} \times x

Multiply the terms with the same base by adding their exponents

45 x^{2 + 1}

Add the numbers

45 x^{3}

45 x^{3} - 18

Solution

9 (5 x^{3} - 2)

Show Solution

Find the roots

x = \frac{3 50}{5}

Alternative Form

x \approx 0.736806

Evaluate

3 x^{2} \times 15 x - 18

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

3 x^{2} \times 15 x - 18 = 0

Multiply

More Steps

Multiply the terms

3 x^{2} \times 15 x

Multiply the terms

45 x^{2} \times x

Multiply the terms with the same base by adding their exponents

45 x^{2 + 1}

Add the numbers

45 x^{3}

45 x^{3} - 18 = 0

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

45 x^{3} = 0 + 18

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

45 x^{3} = 18

Divide both sides

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

Divide the numbers

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

Cancel out the common factor 9

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

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

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

Calculate

x = 3 \frac{2}{5}

Solution

More Steps

Evaluate

3 \frac{2}{5}

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

\frac{3 2}{3 5}

Multiply by the Conjugate

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

Simplify

\frac{3 2 \times 3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 325

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

3 2 \times 25

Calculate the product

350

\frac{3 50}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 3 5^{2}

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

3 5 \times 5^{2}

Calculate the product

3 5^{3}

Reduce the index of the radical and exponent with 3

5

\frac{3 50}{5}

x = \frac{3 50}{5}

Alternative Form

x \approx 0.736806

Show Solution