Solve 3x^(2) 25x-18

Question

Simplify the expression

75 x^{3} - 18

Evaluate

3 x^{2} \times 25 x - 18

Solution

More Steps

Evaluate

3 x^{2} \times 25 x

Multiply the terms

75 x^{2} \times x

Multiply the terms with the same base by adding their exponents

75 x^{2 + 1}

Add the numbers

75 x^{3}

75 x^{3} - 18

Show Solution

Factor the expression

3 (25 x^{3} - 6)

Evaluate

3 x^{2} \times 25 x - 18

Multiply

More Steps

Evaluate

3 x^{2} \times 25 x

Multiply the terms

75 x^{2} \times x

Multiply the terms with the same base by adding their exponents

75 x^{2 + 1}

Add the numbers

75 x^{3}

75 x^{3} - 18

Solution

3 (25 x^{3} - 6)

Show Solution

Find the roots

x = \frac{3 30}{5}

Alternative Form

x \approx 0.621447

Evaluate

3 x^{2} \times 25 x - 18

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

3 x^{2} \times 25 x - 18 = 0

Multiply

More Steps

Multiply the terms

3 x^{2} \times 25 x

Multiply the terms

75 x^{2} \times x

Multiply the terms with the same base by adding their exponents

75 x^{2 + 1}

Add the numbers

75 x^{3}

75 x^{3} - 18 = 0

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

75 x^{3} = 0 + 18

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

75 x^{3} = 18

Divide both sides

\frac{75 x ^{3}}{75} = \frac{18}{75}

Divide the numbers

x^{3} = \frac{18}{75}

Cancel out the common factor 3

x^{3} = \frac{6}{25}

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

3 x^{3} = 3 \frac{6}{25}

Calculate

x = 3 \frac{6}{25}

Solution

More Steps

Evaluate

3 \frac{6}{25}

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

\frac{3 6}{3 25}

Multiply by the Conjugate

\frac{3 6 \times 3 2 5 ^{2}}{3 25 \times 3 2 5 ^{2}}

Simplify

\frac{3 6 \times 5 3 5}{3 25 \times 3 2 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

36 \times 535

Multiply the terms

330 \times 5

Use the commutative property to reorder the terms

5330

\frac{5 3 30}{3 25 \times 3 2 5 ^{2}}

Multiply the numbers

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Evaluate

325 \times 3 2 5^{2}

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

3 25 \times 2 5^{2}

Calculate the product

3 2 5^{3}

Transform the expression

3 5^{6}

Reduce the index of the radical and exponent with 3

5^{2}

\frac{5 3 30}{5 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{5}{5 ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{5 ^{2 - 1}}

Subtract the terms

\frac{1}{5 ^{1}}

Simplify

\frac{1}{5}

\frac{3 30}{5}

x = \frac{3 30}{5}

Alternative Form

x \approx 0.621447

Show Solution