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

Question

Simplify the expression

3 x - 54

Evaluate

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

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms

54 x^{\frac{1}{2}} \times x^{- \frac{1}{2}}

Multiply the terms with the same base by adding their exponents

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

Subtract the numbers

54 x^{0}

Any non-zero expression raised to the power of 0 equals 1

54

3 x^{\frac{1}{2}} - 54

Solution

3 x - 54

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Factor the expression

3 (x - 18)

Evaluate

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

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms

54 x^{\frac{1}{2}} \times x^{- \frac{1}{2}}

Multiply the terms with the same base by adding their exponents

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

Subtract the numbers

54 x^{0}

Any non-zero expression raised to the power of 0 equals 1

54

3 x^{\frac{1}{2}} - 54

Calculate

3 x - 54

Solution

3 (x - 18)

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Find the roots

x = 324

Evaluate

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

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

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

Find the domain

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

Calculate

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

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms

54 x^{\frac{1}{2}} \times x^{- \frac{1}{2}}

Multiply the terms with the same base by adding their exponents

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

Subtract the numbers

54 x^{0}

Any non-zero expression raised to the power of 0 equals 1

54

3 x^{\frac{1}{2}} - 54 = 0

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

3 x^{\frac{1}{2}} = 0 + 54

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

3 x^{\frac{1}{2}} = 54

Divide both sides

\frac{3 x ^{\frac{1}{2}}}{3} = \frac{54}{3}

Divide the numbers

x^{\frac{1}{2}} = \frac{54}{3}

Divide the numbers

More Steps

Evaluate

\frac{54}{3}

Reduce the numbers

\frac{18}{1}

Calculate

18

x^{\frac{1}{2}} = 18

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

(x^{\frac{1}{2}})^{2} = 1 8^{2}

Evaluate the power

x = 324

Check if the solution is in the defined range

x = 324, x > 0

Solution

x = 324

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