Solve 5x root()(3x)-2 root()(3x) -x root()(3x)

Question

Simplify the expression

4 3 x \times x - 2 3 x

Evaluate

5 x 3 x - 2 3 x - x 3 x

Solution

More Steps

Evaluate

5 x 3 x - x 3 x

Rewrite the expression

5 3 x \times x - 3 x \times x

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

(5 - 1) 3 x \times x

Subtract the numbers

4 3 x \times x

4 3 x \times x - 2 3 x

Show Solution

Factor the expression

2 3 x \times (2 x - 1)

Evaluate

5 x 3 x - 2 3 x - x 3 x

Subtract the terms

More Steps

Evaluate

5 x 3 x - x 3 x

Rewrite the expression

5 3 x \times x - 3 x \times x

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

(5 - 1) 3 x \times x

Subtract the numbers

4 3 x \times x

4 3 x \times x - 2 3 x

Rewrite the expression

2 3 x \times 2 x - 2 3 x

Solution

2 3 x \times (2 x - 1)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{1}{2}

Alternative Form

x_{1} = 0, x_{2} = 0.5

Evaluate

5 x 3 x - 2 3 x - x 3 x

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

5 x 3 x - 2 3 x - x 3 x = 0

Find the domain

5 x 3 x - 2 3 x - x 3 x = 0, x \geq 0

Calculate

5 x 3 x - 2 3 x - x 3 x = 0

Subtract the terms

More Steps

Simplify

5 x 3 x - 2 3 x - x 3 x

Subtract the terms

More Steps

Evaluate

5 x 3 x - x 3 x

Rewrite the expression

5 3 x \times x - 3 x \times x

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

(5 - 1) 3 x \times x

Subtract the numbers

4 3 x \times x

4 3 x \times x - 2 3 x

4 3 x \times x - 2 3 x = 0

Factor the expression

2 3 x \times (2 x - 1) = 0

Elimination the left coefficient

3 x \times (2 x - 1) = 0

Separate the equation into 2 possible cases

3 x = 0 2 x - 1 = 0

Solve the equation

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Evaluate

3 x = 0

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

3 x = 0

Rewrite the expression

x = 0

x = 0 2 x - 1 = 0

Solve the equation

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Evaluate

2 x - 1 = 0

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

2 x = 0 + 1

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

2 x = 1

Divide both sides

\frac{2 x}{2} = \frac{1}{2}

Divide the numbers

x = \frac{1}{2}

x = 0 x = \frac{1}{2}

Check if the solution is in the defined range

x = 0 x = \frac{1}{2}, x \geq 0

Find the intersection of the solution and the defined range

x = 0 x = \frac{1}{2}

Solution

x_{1} = 0, x_{2} = \frac{1}{2}

Alternative Form

x_{1} = 0, x_{2} = 0.5

Show Solution