Solve for x (x-5)1/2+5=2

$(x - 5) \frac{1}{2} + 5 = 2$

Step 1

Simplify $(x - 5) (\frac{1}{2}) + 5$ .

Simplify each term.

Apply the distributive property.

$x \frac{1}{2} - 5 (\frac{1}{2}) + 5 = 2$

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

$\frac{x}{2} - 5 (\frac{1}{2}) + 5 = 2$

Combine $- 5$ and $\frac{1}{2}$ .

$\frac{x}{2} + \frac{- 5}{2} + 5 = 2$

Move the negative in front of the fraction.

$\frac{x}{2} - \frac{5}{2} + 5 = 2$

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{2} - \frac{5}{2} + 5 \cdot \frac{2}{2} = 2$

Combine $5$ and $\frac{2}{2}$ .

$\frac{x}{2} - \frac{5}{2} + \frac{5 \cdot 2}{2} = 2$

Combine the numerators over the common denominator.

$\frac{x}{2} + \frac{- 5 + 5 \cdot 2}{2} = 2$

Simplify the numerator.

Multiply $5$ by $2$ .

$\frac{x}{2} + \frac{- 5 + 10}{2} = 2$

Add $- 5$ and $10$ .

$\frac{x}{2} + \frac{5}{2} = 2$

Step 2

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

Subtract $\frac{5}{2}$ from both sides of the equation.

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

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

$\frac{x}{2} = 2 \cdot \frac{2}{2} - \frac{5}{2}$

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

$\frac{x}{2} = \frac{2 \cdot 2}{2} - \frac{5}{2}$

Combine the numerators over the common denominator.

$\frac{x}{2} = \frac{2 \cdot 2 - 5}{2}$

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{x}{2} = \frac{4 - 5}{2}$

Subtract $5$ from $4$ .

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

Move the negative in front of the fraction.

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

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$x = - 1$