Solve 3x^3/2 - 9x^(1/2) -6x^(1/2)

Question

Simplify the expression

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

Show Solution

x_{1} = 0, x_{2} = 5100

Alternative Form

x_{1} = 0, x_{2} \approx 2.511886

Evaluate

(3 \times \frac{x ^{3}}{2}) - 9 x^{\frac{1}{2}} - 6 x^{\frac{1}{2}}

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

(3 \times \frac{x ^{3}}{2}) - 9 x^{\frac{1}{2}} - 6 x^{\frac{1}{2}} = 0

Find the domain

(3 \times \frac{x ^{3}}{2}) - 9 x^{\frac{1}{2}} - 6 x^{\frac{1}{2}} = 0, x \geq 0

Calculate

(3 \times \frac{x ^{3}}{2}) - 9 x^{\frac{1}{2}} - 6 x^{\frac{1}{2}} = 0

Multiply the terms

\frac{3 x ^{3}}{2} - 9 x^{\frac{1}{2}} - 6 x^{\frac{1}{2}} = 0

Subtract the terms

More Steps

\frac{3 x ^{3} - 18 x ^{\frac{1}{2}}}{2} - 6 x^{\frac{1}{2}} = 0

Subtract the terms

More Steps

\frac{3 x ^{3} - 30 x ^{\frac{1}{2}}}{2} = 0

Simplify

3 x^{3} - 30 x^{\frac{1}{2}} = 0

Factor the expression

3 x^{\frac{1}{2}} (x^{\frac{5}{2}} - 10) = 0

Divide both sides

x^{\frac{1}{2}} (x^{\frac{5}{2}} - 10) = 0

Separate the equation into 2 possible cases

x^{\frac{1}{2}} = 0 x^{\frac{5}{2}} - 10 = 0

The only way a root could be 0 is when the radicand equals 0

x = 0 x^{\frac{5}{2}} - 10 = 0

Solve the equation

More Steps

x = 0 x = 5100

Check if the solution is in the defined range

x = 0 x = 5100, x \geq 0

Find the intersection of the solution and the defined range

x = 0 x = 5100

Solution

x_{1} = 0, x_{2} = 5100

Alternative Form

x_{1} = 0, x_{2} \approx 2.511886

Show Solution