Solve x^(2) 3 sqrt(3x)-30

Question

Simplify the expression

3 x^{2} 3 x - 30

Evaluate

x^{2} \times 3 3 x - 30

Solution

3 x^{2} 3 x - 30

Show Solution

3 (x^{2} 3 x - 10)

Evaluate

x^{2} \times 3 3 x - 30

Use the commutative property to reorder the terms

3 x^{2} 3 x - 30

Solution

3 (x^{2} 3 x - 10)

Show Solution

x = \frac{5 8100}{3}

Alternative Form

x \approx 2.016396

Evaluate

x^{2} \times 3 3 x - 30

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

x^{2} \times 3 3 x - 30 = 0

Find the domain

x^{2} \times 3 3 x - 30 = 0, x \geq 0

Calculate

x^{2} \times 3 3 x - 30 = 0

Use the commutative property to reorder the terms

3 x^{2} 3 x - 30 = 0

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

3 x^{2} 3 x = 30

Divide both sides of the equation by 3

x^{2} 3 x = 10

Raise both sides of the equation to the 2 -th power to eliminate the isolated 2 -th root

(x^{2} 3 x)^{2} = 1 0^{2}

Evaluate the power

3 x^{5} = 100

Divide both sides

\frac{3 x ^{5}}{3} = \frac{100}{3}

Divide the numbers

x^{5} = \frac{100}{3}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{100}{3}

Calculate

x = 5 \frac{100}{3}

Simplify the root

More Steps

Evaluate

5 \frac{100}{3}

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

\frac{5 100}{5 3}

Multiply by the Conjugate

\frac{5 100 \times 5 3 ^{4}}{5 3 \times 5 3 ^{4}}

Simplify

\frac{5 100 \times 5 81}{5 3 \times 5 3 ^{4}}

Multiply the numbers

More Steps

Evaluate

5100 \times 581

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

5 100 \times 81

Calculate the product

58100

\frac{5 8100}{5 3 \times 5 3 ^{4}}

Multiply the numbers

More Steps

Evaluate

53 \times 5 3^{4}

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

5 3 \times 3^{4}

Calculate the product

5 3^{5}

Reduce the index of the radical and exponent with 5

3

\frac{5 8100}{3}

x = \frac{5 8100}{3}

Check if the solution is in the defined range

x = \frac{5 8100}{3}, x \geq 0

Solution

x = \frac{5 8100}{3}

Alternative Form

x \approx 2.016396

Show Solution