Solve for x a^2=b^2+c^2-2bx

$a^{2} = b^{2} + c^{2} - 2 b x$

Step 1

Rewrite the equation as $b^{2} + c^{2} - 2 b x = a^{2}$ .

$b^{2} + c^{2} - 2 b x = a^{2}$

Step 2

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

Subtract $b^{2}$ from both sides of the equation.

$c^{2} - 2 b x = a^{2} - b^{2}$

Subtract $c^{2}$ from both sides of the equation.

$- 2 b x = a^{2} - b^{2} - c^{2}$

Step 3

Divide each term in $- 2 b x = a^{2} - b^{2} - c^{2}$ by $- 2 b$ and simplify.

Divide each term in $- 2 b x = a^{2} - b^{2} - c^{2}$ by $- 2 b$ .

$\frac{- 2 b x}{- 2 b} = \frac{a^{2}}{- 2 b} + \frac{- b^{2}}{- 2 b} + \frac{- c^{2}}{- 2 b}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 b x}{- 2 b} = \frac{a^{2}}{- 2 b} + \frac{- b^{2}}{- 2 b} + \frac{- c^{2}}{- 2 b}$

Rewrite the expression.

$\frac{b x}{b} = \frac{a^{2}}{- 2 b} + \frac{- b^{2}}{- 2 b} + \frac{- c^{2}}{- 2 b}$

Cancel the common factor of $b$ .

Cancel the common factor.

$\frac{b x}{b} = \frac{a^{2}}{- 2 b} + \frac{- b^{2}}{- 2 b} + \frac{- c^{2}}{- 2 b}$

Divide $x$ by $1$ .

$x = \frac{a^{2}}{- 2 b} + \frac{- b^{2}}{- 2 b} + \frac{- c^{2}}{- 2 b}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{a^{2}}{(2) b} + \frac{- b^{2}}{- 2 b} + \frac{- c^{2}}{- 2 b}$

Cancel the common factor of $b^{2}$ and $b$ .

Factor $b$ out of $- b^{2}$ .

$x = - \frac{a^{2}}{2 b} + \frac{b (- b)}{- 2 b} + \frac{- c^{2}}{- 2 b}$

Cancel the common factors.

Factor $b$ out of $- 2 b$ .

$x = - \frac{a^{2}}{2 b} + \frac{b (- b)}{b \cdot - 2} + \frac{- c^{2}}{- 2 b}$

Cancel the common factor.

$x = - \frac{a^{2}}{2 b} + \frac{b (- b)}{b \cdot - 2} + \frac{- c^{2}}{- 2 b}$

Rewrite the expression.

$x = - \frac{a^{2}}{2 b} + \frac{- b}{- 2} + \frac{- c^{2}}{- 2 b}$

Dividing two negative values results in a positive value.

$x = - \frac{a^{2}}{2 b} + \frac{b}{2} + \frac{- c^{2}}{- 2 b}$

Dividing two negative values results in a positive value.

$x = - \frac{a^{2}}{2 b} + \frac{b}{2} + \frac{c^{2}}{2 b}$