Precalculus Examples

$x^{2} + y^{2} - 2 x = 0$

Step 1

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

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Step 1.1

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

$y^{2} - 2 x = - x^{2}$

Step 1.2

Add $2 x$ to both sides of the equation.

$y^{2} = - x^{2} + 2 x$

Step 2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{- x^{2} + 2 x}$

Step 3

Factor $x$ out of $- x^{2} + 2 x$ .

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Step 3.1

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

$y = \pm \sqrt{x (- x) + 2 x}$

Step 3.2

Factor $x$ out of $2 x$ .

$y = \pm \sqrt{x (- x) + x \cdot 2}$

Step 3.3

Factor $x$ out of $x (- x) + x \cdot 2$ .

$y = \pm \sqrt{x (- x + 2)}$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 4.1

First, use the positive value of the $\pm$ to find the first solution.

$y = \sqrt{x (- x + 2)}$

Step 4.2

Next, use the negative value of the $\pm$ to find the second solution.

$y = - \sqrt{x (- x + 2)}$

Step 4.3

The complete solution is the result of both the positive and negative portions of the solution.

$y = \sqrt{x (- x + 2)}$

$y = - \sqrt{x (- x + 2)}$

$y = \sqrt{x (- x + 2)}$

$y = - \sqrt{x (- x + 2)}$