Find All Complex Solutions (45-3x)1/2=x-9

$(45 - 3 x) \frac{1}{2} = x - 9$

Step 1

Simplify $(45 - 3 x) \frac{1}{2}$ .

Rewrite.

$0 + 0 + (45 - 3 x) \frac{1}{2} = x - 9$

Simplify by adding zeros.

$(45 - 3 x) \frac{1}{2} = x - 9$

Apply the distributive property.

$45 (\frac{1}{2}) - 3 x \frac{1}{2} = x - 9$

Combine $45$ and $\frac{1}{2}$ .

$\frac{45}{2} - 3 x \frac{1}{2} = x - 9$

Multiply $- 3 x \frac{1}{2}$ .

Combine $- 3$ and $\frac{1}{2}$ .

$\frac{45}{2} + x \frac{- 3}{2} = x - 9$

Combine $x$ and $\frac{- 3}{2}$ .

$\frac{45}{2} + \frac{x \cdot - 3}{2} = x - 9$

Simplify each term.

Move $- 3$ to the left of $x$ .

$\frac{45}{2} + \frac{- 3 \cdot x}{2} = x - 9$

Move the negative in front of the fraction.

$\frac{45}{2} - \frac{3 x}{2} = x - 9$

Step 2

Move all terms containing $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation.

$\frac{45}{2} - \frac{3 x}{2} - x = - 9$

To write $- x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{45}{2} - \frac{3 x}{2} - x \cdot \frac{2}{2} = - 9$

Combine $- x$ and $\frac{2}{2}$ .

$\frac{45}{2} - \frac{3 x}{2} + \frac{- x \cdot 2}{2} = - 9$

Combine the numerators over the common denominator.

$\frac{45}{2} + \frac{- 3 x - x \cdot 2}{2} = - 9$

Combine the numerators over the common denominator.

$\frac{45 - 3 x - x \cdot 2}{2} = - 9$

Multiply $2$ by $- 1$ .

$\frac{45 - 3 x - 2 x}{2} = - 9$

Subtract $2 x$ from $- 3 x$ .

$\frac{45 - 5 x}{2} = - 9$

Factor $5$ out of $45 - 5 x$ .

Factor $5$ out of $45$ .

$\frac{5 (9) - 5 x}{2} = - 9$

Factor $5$ out of $- 5 x$ .

$\frac{5 (9) + 5 (- x)}{2} = - 9$

Factor $5$ out of $5 (9) + 5 (- x)$ .

$\frac{5 (9 - x)}{2} = - 9$

Step 3

Multiply both sides by $2$ .

$\frac{5 (9 - x)}{2} \cdot 2 = - 9 \cdot 2$

Step 4

Simplify.

Simplify the left side.

Simplify $\frac{5 (9 - x)}{2} \cdot 2$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5 (9 - x)}{2} \cdot 2 = - 9 \cdot 2$

Rewrite the expression.

$5 (9 - x) = - 9 \cdot 2$

Apply the distributive property.

$5 \cdot 9 + 5 (- x) = - 9 \cdot 2$

Simplify the expression.

Multiply $5$ by $9$ .

$45 + 5 (- x) = - 9 \cdot 2$

Multiply $- 1$ by $5$ .

$45 - 5 x = - 9 \cdot 2$

Reorder $45$ and $- 5 x$ .

$- 5 x + 45 = - 9 \cdot 2$

Simplify the right side.

Multiply $- 9$ by $2$ .

$- 5 x + 45 = - 18$

Step 5

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Subtract $45$ from both sides of the equation.

$- 5 x = - 18 - 45$

Subtract $45$ from $- 18$ .

$- 5 x = - 63$

Divide each term in $- 5 x = - 63$ by $- 5$ and simplify.

Divide each term in $- 5 x = - 63$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 63}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 63}{- 5}$

Divide $x$ by $1$ .

$x = \frac{- 63}{- 5}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{63}{5}$

Find All Complex Solutions (45-3x)1/2=x-9

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