Algebra Examples

$x + {(y - 1)}^{2} = 0$

Step 1

Subtract $x$ from both sides of the equation.

${(y - 1)}^{2} = - x$

Step 2

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

$y - 1 = \pm \sqrt{- x}$

Step 3

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

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Step 3.1

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

$y - 1 = \sqrt{- x}$

Step 3.2

Add $1$ to both sides of the equation.

$y = \sqrt{- x} + 1$

Step 3.3

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

$y - 1 = - \sqrt{- x}$

Step 3.4

Add $1$ to both sides of the equation.

$y = - \sqrt{- x} + 1$

Step 3.5

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

$y = \sqrt{- x} + 1$

$y = - \sqrt{- x} + 1$

$y = \sqrt{- x} + 1$

$y = - \sqrt{- x} + 1$