Solve 5x^(2) 15x-90

Question

Simplify the expression

75 x^{3} - 90

Evaluate

5 x^{2} \times 15 x - 90

Solution

More Steps

Evaluate

5 x^{2} \times 15 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} - 90

Show Solution

Factor the expression

15 (5 x^{3} - 6)

Evaluate

5 x^{2} \times 15 x - 90

Multiply

More Steps

Evaluate

5 x^{2} \times 15 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} - 90

Solution

15 (5 x^{3} - 6)

Show Solution

Find the roots

x = \frac{3 150}{5}

Alternative Form

x \approx 1.062659

Evaluate

5 x^{2} \times 15 x - 90

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

5 x^{2} \times 15 x - 90 = 0

Multiply

More Steps

Multiply the terms

5 x^{2} \times 15 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} - 90 = 0

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

75 x^{3} = 0 + 90

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

75 x^{3} = 90

Divide both sides

\frac{75 x ^{3}}{75} = \frac{90}{75}

Divide the numbers

x^{3} = \frac{90}{75}

Cancel out the common factor 15

x^{3} = \frac{6}{5}

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

3 x^{3} = 3 \frac{6}{5}

Calculate

x = 3 \frac{6}{5}

Solution

More Steps

Evaluate

3 \frac{6}{5}

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

\frac{3 6}{3 5}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

More Steps

Evaluate

36 \times 325

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

3 6 \times 25

Calculate the product

3150

\frac{3 150}{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{3 150}{5}

x = \frac{3 150}{5}

Alternative Form

x \approx 1.062659

Show Solution