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

Question

Simplify the expression

3 x x - 15 x

Evaluate

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

Subtract the terms

More Steps

Evaluate

- 9 x^{\frac{1}{2}} - 6 x^{\frac{1}{2}}

Collect like terms by calculating the sum or difference of their coefficients

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

Subtract the numbers

- 15 x^{\frac{1}{2}}

3 x^{\frac{3}{2}} - 15 x^{\frac{1}{2}}

Solution

3 x x - 15 x

Show Solution

3 x \times (x - 5)

Evaluate

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

Subtract the terms

More Steps

Evaluate

- 9 x^{\frac{1}{2}} - 6 x^{\frac{1}{2}}

Collect like terms by calculating the sum or difference of their coefficients

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

Subtract the numbers

- 15 x^{\frac{1}{2}}

3 x^{\frac{3}{2}} - 15 x^{\frac{1}{2}}

Calculate

3 x x - 15 x

Rewrite the expression

3 x \times x - 3 x \times 5

Solution

3 x \times (x - 5)

Show Solution

x_{1} = 0, x_{2} = 5

Evaluate

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

Find the domain

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

Calculate

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

Subtract the terms

More Steps

Simplify

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

Subtract the terms

More Steps

Evaluate

- 9 x^{\frac{1}{2}} - 6 x^{\frac{1}{2}}

Collect like terms by calculating the sum or difference of their coefficients

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

Subtract the numbers

- 15 x^{\frac{1}{2}}

3 x^{\frac{3}{2}} - 15 x^{\frac{1}{2}}

3 x^{\frac{3}{2}} - 15 x^{\frac{1}{2}} = 0

Factor the expression

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

Divide both sides

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

Separate the equation into 2 possible cases

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

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

x = 0 x - 5 = 0

Solve the equation

More Steps

Evaluate

x - 5 = 0

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

x = 0 + 5

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

x = 5

x = 0 x = 5

Check if the solution is in the defined range

x = 0 x = 5, x \geq 0

Find the intersection of the solution and the defined range

x = 0 x = 5

Solution

x_{1} = 0, x_{2} = 5

Show Solution